Reactive synthesis for the GR(1) fragment of LTL has been implemented and studied in many works. In this work we present and evaluate a list of heuristics to potentially reduce running times for GR(1) synthesis and related algorithms. The list includes several heuristics for controlled predecessor computation and BDDs, early detection of fixed-points and unrealizability, fixed-point recycling, and several heuristics for unrealizable core computations. We have implemented the heuristics and integrated them in our synthesis environment Spectra Tools, a set of tools for writing specifications and running synthesis and related analyses. We evaluate the presented heuristics on SYNTECH15, a total of 78 specifications of 6 autonomous Lego robots, on SYNTECH17, a total of 149 specifications of 5 autonomous Lego robots, all written by 3rd year undergraduate computer science students in two project classes we have taught, as well as on benchmarks from the literature. The evaluation investigates not only the potential of the suggested heuristics to improve computation times, but also the difference between existing benchmarks and the robot’s specifications in terms of the effectiveness of the heuristics. Our evaluation shows positive results for the application of all the heuristics together, which get more significant for specifications with slower original running times. It also shows differences in effectiveness when applied to different sets of specifications. Furthermore, a comparison between Spectra, with all the presented heuristics, and two existing tools, RATSY and Slugs, over two well-known benchmarks, shows that Spectra outperforms both on most of the specifications; the larger the specification, the faster Spectra becomes relative to the two other tools. Reactive synthesis is an automated procedure to obtain a correct-by-construction reactive system from its temporal logic specification . Rather GR(1) is a fragment of LTL, which has an efficient symbolic synthesis algorithm , 42 and In this work we present and investigate performance heuristics for algorithms for GR(1) synthesis in case a specification is realizable and Rabin(1) synthesis , 39 in cAll heuristics we have developed and studied, satisfy two main criteria. First, they are generic, i.e., they are not optimized for a specific specification or family of specifications. Second, they are conservative, i.e., none of the heuristics changes the results obtained from the algorithms.We have integrated the heuristics in our synthesis environment Spectra Tools, available together with a set of Eclipse plugins for writing specifications and running synthesis and related analyses, see .We evaluate the presented heuristics on three sets of specifications. The first set, SYNTECH15, consists of 78 specifications of 6 autonomous Lego robots, and the second set, SYNTECH17, a total of 149 specifications of 5 autonomous Lego robots, both written by 3rd year undergraduate computer science students in two project classes we have taught. The third set consists of specifications for the ARM AMBA AHB Arbiter (AMBA) , 30, 48.A preliminary version of the present work has appeared in . The preThe remainder of this work is structured as follows. Section We breifly provide necessary background on LTL and synthesis, X (next) and U (until).We repeat some of the standard definitions of linear temporal logic (LTL), e.g., as found in , a modalith position. For position i we use i, inductively defined as:We denote F , G , and H  defined as:LTL formulas can be used as specifications of reactive systems, where atomic propositions are partitioned and interpreted as either environment (input) or system (output) variables. An assignment to all variables is called a state.The syntax of LTL formulas over I, prescribes the outputs of a system for all environment choices, such that all computations from I will satisfy I if there is a winning strategy on I. The winning states are all states W such that the system wins on W.A winning strategy for an LTL specification A specification S, i.e., the values of fixed-points are subsets of S. For monotonic functions S| iterations due to monotonicity of The number of iterations of the fixed-point computation is linear in |S|. When states are represented by a set of atomic propositions (or Boolean variables) AP then AP. Because the least (greatest) fixed-point is unique and The modal nt logic . It exteratively  in at moGR(1) synthesis  handles Note that realizing (satisfying) a justice assumption (guarantee) GFGFA GR(1) synthesis problem consists of the following elements :\documenR by , also called the controlled predecessors, defined as:Y are not computed independently for each Z; instead the value of Z is updated before computing GR1) synthesis has the following notion of (strict) realizability  defined  synthesiented in , 42. Thethm from  for comptruction .A specification nd Sa’ar  show an entclass1pt{minimaR by defined as:We denote the states from which the environment can force the system to visit a state in Z in line 18. Algorithm 2 stores intermediate computation results in arrays Z (line 19) and X (line 13) for strategy construction.The algorithm from  (extende in JTLV ) for comn of Eq. , e.g., tAll the computations and algorithms described above are done symbolically using Boolean functions. The most common way to represent Boolean functions is using Binary Decision Diagrams (BDDs), introduced in . The conO(nlog(n)) where n is the number of variables. From now on we will refer to the canonical form of an ordered BDD simply as BDD.Another important rule to adhere to for efficiency is variable ordering, meaning imposing a single occurrence of a Boolean variable along any path in the DAG. Such BDD is called ordered BDD. A reduced ordered BDD that represents a given function is unique, hence we can say that an ordered BDD has a canonical form. All the BDD operations are done on the canonical forms, and binary operations are done on BDDs with compatible variable order. Since the operations may result not in the canonical form of an ordered BDD, the last step is always applying the reduction rules. The reduction on an ordered BDD is essentially a bottom-up DAG traversal, and it takes TRUE and FALSE nodes in not and then(x) respectively.restrict), sub-tree of then(x)). This can be generalized to nested quantifiers in a straightforward way, though the nested problem is NP-complete. We denote this by exists algorithm, we need to compute  algorithn in Eq. , which iR;R;Given an unrealizable GR(1) specification, an unrealizable core is a locally minimal subset of system guarantees for which the specification is unrealizable . Such a E for a given monotonic criterion check. We show the DDMin algorithm in Algorithm 6. The input of the algorithm consists of a set E and the number n of parts of E to check. The algorithm starts with E and n in recursive calls according to different cases . The computation starts by partitioning E into n subsets and evaluating check on each subset part (line 1) and its complement (line 7). If check holds (line 2 or line 7), the search is continued recursively on the subset part (or its complement), until part (or its complement) has no subsets that satisfy check. If check neither holds on any subset part nor on the complements, the algorithm increases the granularity of the partitioning to 2n (line 14) and restarts.The delta debugging algorithm  (DDMin) part of system guarantees. To compute an unrealizable core using DDMin, the method check performs a realizability check for the given subset and  and related algorithms. We divide the presented heuristics into three lists. The first list is inspired by classic heuristics for the controlled predecessor computation, i.e., the evaluation of the operators d Sect. . The secd Sect. . Finallyd Sect. . For eacRationale The size of the BDDs depends greatly on the variable order. During the computations the BDDs may grow to the extent that they cannot be computed in a reasonable time if at all, even for small examples. To reduce the BDDs sizes we use dynamic reordering that is supplied by the CUDD package. The CUDD package uses the SIFT algorithm (presented in  (Rabin(1), Z[cz]). Starting in the second iteration of the outermost fixed-point we compare for each justice Z of its iteration to the previously computed Z[j] (Rabin(1), Z[Z. The heuristics is correct since the next iteration of justice j] (Rabin(1), Z[k]=Z[j] (Z]RationalThe time complexity of a straightforward implementation of the fixed-point computation is cubic in the state space and can be reduced to quadratic time , as mentHeuristics Fixed-points are usually computed by fixed-point iteration starting from Z, and iteration l of Y: due to monotonicity X for X for  idea of  is to exk+1 .In both, the GR(1) algorithm and the Rabin(1) algorithm, the fixed-point computations also depend on justice assumptions X in line 9. Unless the algorithm computes the first iteration of Z the value of X is set to the previously computed result for the same justice assumption cy of Y, i.e., X is set to memory cell X[j][i][cy] intersected with Z. This value is an over-approximation of the greatest fixed-point X and its computation likely terminates after fewer iterations.We implemented this heuristics in the GR(1) game Algorithm 1 with a modified start value for the fixed-point computation of X in line 10. Unless the algorithm computes the first iteration of Z the value of X is set to the previously computed result for the same justice assumption Y. This value is an under-approximation of the least fixed-point X and its computation likely terminates after fewer iterations. Note that in Algorithm 2 the fixed-point value of X is only stored for the last iteration of Y (line 13). We had to change the implementation to store X for all iterations of Y to use fixed-point recycling as described in  in Algorithm 1, line 19 in the last fixed-point iteration of Z. Thus, Y and we change the initialization of Y in line 4 to Only safety guarantees were removed from parent: We can reuse all information of the previous computation up to the first removed justice guarantee. We reuse the memory Z on parent up to the first removed justice guarantee. Then we continue the computation.Only justice guarantees were removed from Case 2: All subsets part of parent are realizable and DDMin continues with complements in Algorithm 6, line 7: In this case and for Z to the intersection of system winning states Z to the union of environment winning states Case 1: An unrealizable subset Case 3: All subsets and complements are realizable and DDMin increases search granularity in Algorithm 6, line 14: For the new run Case 1 applies (with the previous parent) and Case 2 applies when checking complements of the sets with higher granularity.Intuition As an example, this heuristics is effective when different checked subsets have disjoint winning states and their subsets are checked. Here, Case 2 would immediately detect unrealizability. From the case distinction, it is possible to see that there are executions of the DDMin algorithm where the heuristics does not contribute, e.g., in Case 1 when justice and safety guarantees are removed .It is important to note that this heuristics comes at the price of possibly large amounts of additional memory . The increase in number of BDDs kept in memory may make dynamic variable reordering more frequent and more time consuming.Rationale In Sect. Heuristics The implementation of this heuristics is based on the implementation in Sect. The pre-processing for DDMin has a list of all the support sets of the BDDs of the safety guarantees. Using this list we look for partitions as described in Sect. Intuition The heuristics is effective when the DDMin algorithm requires many realizability checks with large numbers of guarantees. Then the partitioning and order of all guarantees computed at the start is reused many times and prevents repeated individual preprocessing for the partitioned transition relation of Sect. Rationale GR(1) games and Rabin(1) games are determined: each game is either unrealizable for the system player or unrealizable for the environment player. To check for unrealizability, it is thus equally possible to play the Rabin(1) game or the GR(1) game.The implementations of Könighofer et al.  and CimaHeuristics We replace the implementation of check. Instead of playing the GR(1) game we play the Rabin(1) game and negate the result.Intuition Although one algorithm computes exactly the complement set of winning states computed by the other, and the worst-case number of iterations is the same for both, for specific specifications, the number of iterations and/or the computation time of each step may differ.We divide the evaluation into three parts following the division of the performance heuristics into heuristics for controlled predecessor computation and BDDs from Sect. ...when applied to specifications with different original running times?...individually and together?...when applied to specifications from different sets?Finally, while the main goal of our work is not to outperform existing GR(1) synthesizers but to formally define and empirically investigate a list of suggested heuristics, in order to put our results in context, we present a comparison against two previously presented tools, RATSY [RQ4How does the performance of our implementation in Spectra, with all heuristics employed, compare against the performance of previously presented tools?The evaluation aims to address the following three research questions. How effective are the heuristicss, RATSY  and Slugs, RATSY . Thus, wWe used the GR(1) game and Rabin(1) game implementations shown in Algorithm 1 and Algorithm 2 as reference  would not consider redundant BDDs in the ordering.For the evaluation of the first three research questions, we implemented a test frame that executes a realizability check or the DDMin algorithm using GR(1) or Rabin algorithms with different heuristics, as specified to the test, and measures the running times in nanoseconds. We executed each test for every specification 50 times  specifications are available and these were usually created by authors of synthesis algorithms or extensions thereof.For the purpose of evaluation, we have collected specifications created by 3rd year undergraduate computer science students in two project classes that we have taught. Over the course of a semester, the students have created specifications for real systems, which they actually built in Lego and run throughout specification development   and a GeFor the evaluation of the first three research questions, we included 5 different sizes of AMBA (1 to 5 masters) and 5 different sizes of GenBuf (5 to 40 requests), each in its original version plus the 3 variants of unrealizability described in   and 10 different sizes of GenBuf (5 to 90 requests), each in its original version (as given in ) plus thFor details on the specification sizes see Appendix To validate our intuition on the working of the heurisitics and their speedup, for each of the heuristics we have created one example specification where the heuristics is very effective and one example specification where it does not yield an improvement of performance. We run Spectra over these example specifications, with and without the respective heuristics, and validated that the better or worse performance is indeed observed as expected.While these examples are synthetic, artificial specifications, they provide concrete instances that strengthen our confidence and intution about the working of each of the heuristics. We made all these example specifications available and documented as part of the supporting materials for the paper in .Our implementation of the different heuristics might have bugs, so to ensure correctness of the code we performed the following validations.BDDs count The BDDs are referenced and de-referenced with each usage. To make sure that we do not have inconsistencies in our data structure we used validations of CUDD (like Cudd_DebugCheck and Cudd_CheckKeys).Winning states The set of winning states that are computed in Algorithms 1–2 for realizable specifications should not be affected by the heuristics. We ensure it by computing the complete set of winning states using the original algorithms and comparing the results to the winning states computed by the modified algorithms employing each of the heuristics from Sect. Game memory We need to ensure that the game memory allows for strategy construction (memory is different for fixed-point recycling). For that, we have synthesized strategies from the game memory produced when using our heuristics. We then verified the correctness of the strategies by LTL model checking against the LTL specifications for strict realizability of the original GR(1) and Rabin(1) specifications.Controlled predecessors For the partitioned transition relation from Sects. and , against the result of the original computations with the single transition. Since we get the same set of states, the partitioning and the revised computation of the controlled predecessors are correct.Unrealizable core For the DDMin heuristics from Sect. We run the validation implementation once and did not include it in the total running times reported in the evaluation results. Validation using all the above techniques was successful on all 267 specifications used in this work. This provides evidence for the correctness of the heuristics and their implementations.sca means that for 50% of the specifications for which the original GR(1) implementation takes more than 5 s, the sca heuristics performs at least 1–0.68 all, the value 0.40 means that for 50% of the specifications for which the original GR(1) implementation takes more than 5 s, using all three heuristics together improves performance by at least 1–0.4 We now present aggregated running time data from all runs on all specifications with the different heuristics and their combination. We decided to present for all experiments minimum, maximum, and quartiles of ratios. The ratios are of the different heuristics running times to the original running times of the GR1) game Algorithm 1, the Rabin(1) game Algorithm 2, and DDMin Algorithm 6. For example, the value 0.68 in Table  game AlgFor each set of the heuristics presented in Sects. Original running times dissection A set of four tables that present a dissection of the ratios of running times of a given algorithm according to the original running times: two tables for specifications that a given algorithm runs for less then 5 s and for more than 5 s, then two tables for specifications that a given algorithm runs in 5 to 30 s, and in more than 30 s. The tables show the ratios of the different heuristics running times to the original running times as explained above. Tables Specification dissection A set of three tables that present the ratios of running times for heuristics separately for realizable and unrealizable specifications from the sets SYNTECH15, SYNTECH17, and AMBA and GenBuf. The tables show the ratios of the different heuristics running times to the original running times, as explained above. Tables We have run all experiments described above separately for the GR(1) algorithm and for the Rabin(1) algorithm. In almost all experiments, the effect of the heuristics on the performance of the two algorithms was very similar. Thus, to make the presentation concise, below we only report the results for the GR(1) algorithm and mention the results for the Rabin(1) algorithm in footnotes, only in a few cases where they are indeed different. The complete results for the Rabin(1) algorithm are available together with all other results in .In the remainder of this section, Sect. grp is grouping of variables and their primed copies from Sect. sca is the combined conjunction and existential abstraction from Sect. prt is the partitioned transition relation from Sect. all we refer to the use of all these heuristics together.We present the ratios of running times for heuristics from Sect. RQ1: Effectiveness of heuristics with regard to different original running times For the GR(1) algorithm, for 82% of the specifications, realizability checking completes in less than 5 s, and for these (Table grp). On the other hand, it has a negative effect on 50% of the specifiacations. The combined conjunction and existential abstraction (Sect. sca). The partitioning of the transition relation  improves running times by at least 60%.For specifications that take more than 5 s Table , we see on Sect.  improveson Sect.  improvesMoreover, the partitioning of the transition relation is typically more effective as the original running time increases. For 50% of the specifications that originally run for 5 to 30 s Table , the impRQ2: Effectiveness of heuristics individually and together The heuristics of grouping variables and their primed copies reduces running times by at least 5% on 25% of both realizable and unrealizable specifications for the GR(1) algorithm (Table grp). Also, for this heuristics we see the worst maximal running time ratio.sca) that it performs better for 75% of the specifications by at least 22%.6The combined conjunction and existential abstraction Sect. , when apprt). This might be due to the overhead described in Sect. 7The heuristics of the partitioned transition relation appears ineffective for most realizable and unrealizable specifications (column RQ3: Difference between specification sets The SYNTECH17 specifications are the only ones for which we see a positive effect with the partitioned transition relation heuristics (column prt). For 25% of both realizable and unrealizable specifications, we see 13–17% improvement in running times. This can be attributed to the nature of the specifications as described in Sect. all) the running times decreases by at least 42%. This might be due to this set of specifications being the largest unrealizable set, which also contains the largest percentage of large (and slow) specifications. In comparison, for the set of SYNTECH15 specifications we observe almost no improvement, and this is the set of the smallest (and fastest) specifications.For AMBA and GenBuf we get the greatest improvement in running times for 25% of the unrealizable specifications. For all of the heuristics combined  fixed-point algorithm  are faster by at least 9%. However, for 25% of the specifications that take longer than 5 s to complete, all the heuristics combined improve the running time by at least 30%, and for 75% of these specifications we see an improvement by at least 8% in running time.hm Sect.  have somhm Sect. . For 25%eun), for 25% of the specifications that originally take more than 30 s, the running times improve by at least 58% for, while for 25% of the specifications that take 5 to 30 s the improvement is only by at least 10%. This result is a bit misleading since most of the specifications that originally take more than 30 s are unrealizable, so it entails that early unrealizability detection will perform better for this case.For specifications whose original running time is greater than 5 s, most of the heuristics have similar effect, regardless of the increasing original running times. For early detection of unrealizability , but seems even less effective on unrealizable specifications. As expected, the early detection of unrealizability has no notable effect on realizable specifications (Table eun), but on unrealizable specifications reduces running times of 50% of the specifications by at least 12%/8%/46%. The heuristics of fixed-point recycling appears ineffective for unrealizable specifications, but reduces running times of 25% of the realizable specifications by at least 7%/16%/17% (Table fpr). As good news, the combination of all heuristics typically improves over each heuristics separately .8ns Table , efp, buns Table , eun, buRQ3: Difference between specification sets For realizable specifications, we see that the suggested heuristics perform better on the AMBA and GenBuf set and SYNTECH17 set than on SYNTECH15, i.e., for GR(1) algorithm all heuristics  decreases running times on 50% of the AMBA and GenBuf and SYNTECH17 specifications by at least 9%, and for SYNTECH15 specifications by at least 5%. A more significant difference between the specification sets is observed for unrealizable specifications. Here the speedup for 50% of the specifications, mainly obtained by eun, is at least around 10% for SYNTECH15 and around 7% for SYNTECH17 but at least around 50% for AMBA and GenBuf. We believe that this difference is due to the systematic and synthetic reasons for unrealizability added by Cimatti et al. [i et al. .opt1 is all the heuristics from Sects. opt2 is the heuristics from opt1 with the heuristics for partitioned transition for DDMin from Sect. sets is the contained sets in the core computation from Sect. inc is the incremental algorithm for similar candidates from Sect. all we refer to the combination of sets and opt2, since opt1 is contained in opt2 and inc does not seem to improve running times.We present the ratios of running times for heuristics from Sect. RQ1: Effectiveness of heuristics with regard to different original running times The core computation heuristics  are faster by at least 9%. There is a notable effect on specifications that are slower than 30 s. For all the specifications the DDMin is faster by at least 57%. There are few specifications for which the DDMin did not complete until the cutoff time (24 h), and for these we count the original running time as 24 h. For this reason we have ratios that show improvement of 99%.cs Sect.  have somcs Sect. . For 25%opt1). For specifications that run originally for 5 to 30 s, the running time is faster by at least 67% for 50% of the specifications, and for all the specifications that run longer than 30 s the running time is better by at least 68%.All the heuristics combined from Sects. sets). It is most effective for specifications with original running time from 5 to 30 s. For 50% of the specifications there is an improvement of 24%. This heuristics is less effective by itself on large specifications since the first iterations run on very large sets, and without any performance heuristics for these expensive realizability checks we get running times close to the original ones. However, we can see an effect in the combination of all the heuristics . For 50% of the specifications with original running time greater than 30, the improvement in running times is at least 94%, where without contained sets heuristics (column opt2) there is an improvement of at least 86%.The contained sets heuristics Sect.  shows leFinally, for the incremental algorithm for similar candidates Sect. , for 25%9RQ2: Effectiveness of heuristics individually and together Using the combined heuristics  appears effective on all specifications and reduces running times for 60% of the specifications  has at least 4% improvement for 25% of the specifications.The heuristics of contained sets (column opt1 and opt2 seem to be the most effective for most specifications. The difference between them is that in opt1 the partitioning of the transition relation is performed in each iteration of Algorithm 6 (in check), but in opt2 the partitioning is done in the pre-processing  implementation (Table opt1 and by 19% with opt2. This means that the partitioning and the order of quantifications that is found in every iteration of DDMin (for different sets) might be less expensive in computation time than computing it once in the pre-processing stage and then searching for the information in every iteration of DDMin.The heuristics of ng Sect. . We can inc). It does yield a small improvement for SYNTECH17 of 6% for DDMin.Contrary to our expectation, the reuse of previous BDDs for incremental game solving does not improve running times for almost all specifications . This can be attributed to the increasing original running times. Another observation is that the reuse of previous BDDs for incremental game solving is beneficial only for SYNTECH17 specifications. It is interesting since it is the only set of specifications that has large specifications that were not created systematically.RQ1: Effectiveness of heuristics with regard to different original running times For all the heuristics presented in this work, it is apparent that for specifications where the original running time is greater than 5 s, there is a great improvement. For all the heuristics of controlled predecessor computation and BDDs . The SYNTECH15 set typically shows the least improvements for most of the heuristics, and it is the set of the smallest specifications. The SYNTECH17 set has larger specifications and it shows better results than SYNTECH15 for most of the heuristics. Both SYNTECH15 and SYNTECH17 were created by students in a project class for the development of Lego robots  SYNTECH15, which are specifications created by students for different robotic systems, (2) SYNTECH17, which are also specifications created by students but with an improved set of tools, and (3) the AMBA and GenBuf specifications, which were created by researchers and systematically scaled to larger sizes. The total number of the specifications might be insufficient. The set SYNTECH15 consists of 78 specifications . The set SYNTECH17 consists of 149 specifications . The set AMBA and GenBuf consists of 40 specifications .We share some observations on the sets of specifications that might have an influence on the generalizability of the results. First, the AMBA and GenBuf specifications used in the literature were generated systematically for growing parameters (number of AMBA masters and GenBuf senders). Thus the 40 AMBA and GenBuf specifications essentially describe only two systems. Furthermore, the reasons for unrealizability of AMBA and GenBuf were introduced artificially and systematically  and consSecond, the running times for checking realizability of the SYNTECH15 specifications are rather low and range from 1.5 to 1300 ms, with median around 30 ms. In this set the specifications are biased based on the numbers of revisions committed by students during the work on the project: the Humanoid has 21 specifications , the Gyro has 11 specifications , and the SelfParkingCar has only 4 specifications in total.Finally, the SYNTECH17 specifications are larger, but the realizability check on 75% of them is still quite fast and takes less than 4 s. The maximal running time is about 8.5 s. There also might be slight bias towards specific sets of specifications: the SIMPLECar has 45 specifications , the AirportShuttle has 32 specifications , the Elevator has 26 specifications , the RobotArm has 26 specifications , and the ConvoyCars has 20 specifications .We showed in Sect. We mitigate the above concerns by having on one hand specifications like AMBA and GenBuf that were written by researchers systematically, where we can see the effect of the heuristics on growing specifications, and on the other hand, the SYNTECH15 and SYNTECH17 specifications, which were not created systematically and describe 11 very different Lego robot systems. Also each system has different specifications that are a result of different revisions and they can be very different from one another.Finally, none of the specifications were written by engineers in an industrial setting, so we cannot evaluate how our results may generalize to large scale real-world specifications in practice.Despite all the above, it is important to note that in comparison to related works in the field of GR(1) synthesis, the set of specifications that we used for the evaluation is rather large and diverse.We discuss related works that deal with BDD variable reorder and other performance heuristics for reactive synthesis and DDMin.BDD variable reorder It is well known that the order of BDD variables heavily influences the performance of BDD-based algorithms [gorithms , 51. A lgorithms  discussegorithms  found thOur experience showed similar results. Any static reordering heuristics and experiments with employing dynamic reordering at different points did not compare to the dynamic reordering presented by Rudell  and implPerformance heuristics for reactive synthesis A number of heuristics for BDD-based safety game solvers have been reported as outcome of the SYNTCOMP reactive synthesis competitions [in Algorithm 1 and in Algorithm 2). We employ similar ideas of reordering, eager BDD deallocation, combined conjunction and existential abstraction, and transition partitioning. In addition, we implement heuristics at the level of fixed-points and repeated computations, which were not discussed there. Notably, an approach for predicate abstraction for predecessor computation has already been implemented for GR(1) synthesis [etitions –25. Mostynthesis , 50, andPartitioned transition relation was used in several works , 24, thoPerformance heuristics for DDMin Könighofer et al. [r et al.  presenteStrategy construction Others have focused on strategy construction for GR(1). Strategies are constructed from the memory stored in the X, Y, and Z arrays in Algorithm 1 and Algorithm 2. Schlaipfer et al. [r et al.  suggest r et al.  discuss Performance heuristics for specifications Finally, as a very different and complementary approach to ours, one can consider rewriting the GR(1) specification to speed up realizability checking and synthesis. Filippidis et al. [s et al.  report os et al.  to use fWe presented a list of heuristics to potentially reduce running times for GR(1) synthesis and related algorithms. The list includes efficient computations of the controlled predecessors and BDD level operations, specifically grouping of variables and their primed copies, combined conjunction and existential abstraction, and use of partitioned transition relation. It further includes fixed-point related heuristics, specifically early detection of fixed-points, early detection of unrealizability, and fixed-point recycling. Finally, it includes heuristics for accelerating unrealizable core computation.We have implemented the heuristics and integrated the implementation in the Spectra synthesizer, part of Spectra Tools, a set of tools for writing specifications and running synthesis and related analyses, see .We evaluated the heuristics and their combination on three sets of benchmarks, first SYNTECH15, a set of 78 specifications created by 3rd year undergraduate computer science students in a project class of one semester, second SYNTECH17, a set of 149 specifications created in a repetition of the class, and finally on the two systems, AMBA and GenBuf, which are well-studied in the GR(1) literature. All specifications used in our evaluation, the raw data recorded from all runs, and the program to reproduce our experiments are available from .Our evaluation shows that most heuristics have a positive effect on running times for checking realizability of a specification and for unrealizable core computation. Most importantly, their combination outperforms the individual heuristics, even though there is a risk that some heuristics will increase the running time. It is evident that the greatest improvement is for specifications that have slower original running times. This is a positive result, as these specifications are the ones it is most important to address in order to make GR(1) and related algorithms more useful and applicable in practice.Moreover, our evaluation shows that the Spectra tool outperforms the two previously published tools, RATSY and Slugs, on large specifications. For small specifications, the overhead of the pre-processing computations is too large compared to the running time of the original implementation. However, the positive effect of the heuristics increases as the specifications grow in size, i.e., the larger the specification, the faster Spectra becomes relative to the two other tools.We consider the following future research directions. First, one may better investigate why some heuristics do not work well in general and on particular specifications. Perhaps some specifications have special characteristics that make them resist some of the heuristics we have considered. Such an investigation may result in suggestions for additional heuristics, including ones that assist in predicting, given a specification, which if any heuristics may be applied to it successfully.Second, one may consider the application of the same heuristics to other GR(1) related algorithms, including, e.g., identifying non-well-separation and computing non-well-separation core , repair Third, we consider further evaluation over additional sets of specifications, both synthetic and real. It may be interesting to evaluate Spectra against the specifications used in the series of SYNTCOMP competitions –25. NoteFinally, it may be interesting to collect and report not only running time performance data but also iteration depth and memory usage data, specifically comparing the effect of the different heuristics on each of these. Intuitively, we expect the combined conjunction and abstraction heuristics from Sect. Our work is part of a larger project on bridging the gap between the theory and algorithms of reactive synthesis on the one hand and software engineering practice on the other. As part of this project we are developing the Spectra specification language  and new


This paper describes the current state-of-the-art in fatigue life assessment for lightweight composite structures with the use of the frequency domain fatigue life calculation method. Random stationary gaussian loading signals have been generated and served in the process of fatigue calculation. The material information that is being used in the calculation process has been obtained from literature for the Glare 2 composite. The effect of nonzero mean stress and different fiber orientations have been taken into account. The calculations have been performed for two mean stress compensation models by Goodman and Gerber. The proposed procedure gives satisfying results for the high-cycle fatigue region for Goodman and an overall good comparison in both regimes for the Gerber model. The purpose of the work was to analyze the effect of the nonzero mean stress value on the fatigue lifetime estimation method defined in the frequency domain in hybrid materials. The analysis of the mean stress effect plays an important role when estimating the fatigue life of materials due to the fact that it can be considered as an extra static load added to the system. This can be also analyzed as an effect of prestressing the composite material, which is analyzed with the crack propagation approach by many scientists like Park et al.  or Guo eIn the present paper the mean stress effect compensation was analyzed for materials consisting of three layers of aluminum and two layers of Glass Fiber Reinforced Polymer (GFRP). For this purpose, two different models were used for three different fiber orientations—θ = 0°, θ = 5°, and θ = 10°. Another important aspect was the comparison between rainflow and frequency domain methods for the high and low-cycle fatigue regime. Fatigue lifetime prediction is a constantly developing area for Carbon Fiber Reinforced Polymer (CFRP) materials as we can notice by the number of publications .Issues related to the determination of fatigue life of materials have been analyzed for many years. The fact of material cracking due to cyclic loads with an amplitude much smaller than the maximum static stress value was observed for the first time in the 19th century .At the beginning, fatigue was mainly analyzed in isotropic materials, such as steel. However, with the passage of time and the development of materials, fatigue was also analyzed in modern materials, including those of an anisotropic nature. Nowadays when designing elements, a lot of emphasis is put on lightweight structures, such as those made of composite laminates or fiber-metal laminates, for which classic methods used for e.g., steel cannot be used.The fatigue phenomenon in lightweight structures is a complex matter and many factors are causing it. We can divide these factors into material microscopic structure as well as loading conditions and working forces. In terms of this research, we are going to discuss the problem of static forces acting on the whole structure. This is the case of nonzero mean stresses that are acting on the structures. The own weight of the construction as well as a static force acting on the lightweight structure may influence its fatigue life enormously. During the fatigue life assessment process, it is crucial to take into account cases of nonzero mean stresses. We have to compensate this effect in some kind of way. The main solution that is used is based on the idea of amplitude transformation in terms of mean stress. This idea works well for the case of algorithms defined in the time domain, but in the case of frequency domain algorithms we need to use a different path. This path includes a transformation process of the power spectral density (PSD) and works well for metallic materials. There are no papers analyzing this method for composite materials with the effect of nonzero mean stress. The aim of this paper is to perform a simulation of fatigue life assessment for a randomly generated signal and material constants taken out of the literature for composite materials under nonzero mean stresses. In order to understand the idea behind amplitude transformation, we need to define some basic definitions used in the process.maxσ and minσ are the maximum and minimum stress.Stress amplitude can be defined as (Equation (1)): The mean stress can be defined as (Equation (2)):Another important feature related to loading conditions is the stress ratio R. Some interesting cases of this ratio are presented in aTσ is the transformed stress amplitude and Rm is the ultimate tensile strength.The nonzero mean stress has a huge effect on the fatigue life and is often taken into account in the transformation process of stress amplitudes. These transformations can be presented in the form of normalized graphs in terms of mean stress to ultimate strength and stress amplitude to transformed amplitude with many literature models, as presented in This model is linear, but we can also use a parabolic model proposed by Gerber , which cIn this study, results of fatigue lifetime for different types of the GLARE 2 materials were analyzed. The results of experimental tests have been taken from the paper by Kawai and Kato . In geneIt can be assumed that FML materials use the best features of both composite and metal materials. It is assumed that individual components of FML materials eliminate each other′s disadvantages. The use of FMLs results in e.g., better fatigue life or improvement of fire-retardant properties. The external metal layers in FMLs protect the internal part of the laminate by compensating mechanical impact and also hydrothermal influence , meanwhiIn this special case, the material consists of alternating layers of epoxy reinforced with unidirectional fibers and layers of aluminum alloy, as shown in Strength in the axis parallel to the fibers X = 1144 MPa;Strength in the axis perpendicular to the fibers Y = 261 MPa.In the literature  that wasAs was introduced, in GLARE 2 materials, two layers of material are made of GFRP in which the epoxy resin is used as a matrix, while the continuous glass fiber is applied as reinforcement. However, the direction of fiber arrangement in the layer relative to the x direction marked in Al/GFRP θ ≡ 0°/Al/GFRP θ ≡ 0°/Al;Al/GFRP θ ≡ 5°/Al/GFRP θ ≡ 5°/Al;Al/GFRP θ ≡ 10°/Al/GFRP θ ≡ 10°/Al.When the angle θ between fiber direction and the x direction is 0° ≤ θ ≤ 15°, the fatigue fracture has a type of fracture corresponding to the composite material. However, when 30° ≤ θ ≤ 90°, the fatigue fracture in the FML is characterized by the fracture of aluminum alloy. In this case, just the situation of the fatigue failure for the composite has been analyzed, which means that just the cases of θ ≡ 0°, θ ≡ 5°, and θ ≡ 10° have been analyzed. As a result, three different types of specimens have been taken into account:Based on the S–N curves and failure criteria;Residual strength models;Progressive fatigue damage models.When analyzing the fatigue lifetime for composite materials there are three different models that can used :Based onOne of the proposals of predicting the fatigue life was proposed by Zhou and Wu . They adIn the literature, there may also be found tests where the influence of the temperature on the fatigue life was tested. Song et al.  tested fRunning only in the metal part;Resulting delamination between the metal and the fibrous layer.The fatigue life in the special form of lightweight structures—fiber-metal laminates—was also separately analyzed. In FMLs, just as in other hybrid materials, the phenomenon of fatigue crack initiation is said to be associated with a metal component, and crack initiation occurs in the same conditions as the initiation in solid metal material . Next, tTherefore, they were analyzed as separate fracture mechanisms. The type of fracture mechanism depends on the rate of release of the deformation energy, which is also influenced by the interface geometry and the percentage of fibers in the composite layer. The fatigue process for composite materials may also be divided into two parts—the first for the crack initiation and the second for the crack propagation. The methods used in this paper refer to the first part where crack initiation is the final frontier for fatigue.When the angle θ between fiber direction and the x direction is 0° ≤ θ ≤ 15°, the fatigue fracture has a type of fracture corresponding to the composite material. However, when 30° ≤ θ ≤ 90°, the fatigue fracture in the FMLs is characterized by the fracture of aluminum alloy. In this case, just a situation of the fatigue failure as for the composite.Rx is the autocorrelation function.Fatigue life assessment techniques are set either in the time or frequency domain. Those set in the time domain are called the cycle counting methods and use algorithms for cycle counting. The most famous method, developed by Endo  and wideTo calculate the spectral moments we can use the Equation (7)We need to remember that in the case of nonzero mean stresses we need to perform a PSD transformation; in many terms, a correction to the PSD with the use of the Equation (8) proposed by Niesłony and Böhm :(8)GσTN):This method has been compared with the rainflow cycle counting method and the results have been presented in the next chapter.One of the most important parts in the process of fatigue life estimation is the proper use of fatigue curve data, such as the crack propagation curves as presented by Guo et al.  or S–N cThe next step was the random signal generation with nonzero mean stress. The signal had to have a gaussian and stationary characteristic in order to be used directly within the frequency domain. A random signal that suited these assumptions has been generated with the global value of R = 0.1 and a section of this signal is presented in This signal has been directly taken for calculations for rescaled global maximum amplitudes with the use of the rainflow method. In order to calculate the fatigue life, we needed to transform the original signal in order to set a zero mean stress value, but we needed to remember the original mean stress in order to take it into account in the compensation process. In this case, we obtained a global zero mean stress history as presented in The Welch PSD estimate of the generated random signal after zeroing the mean is presented in The comparison of results obtained with the rainflow and the Dirlik model together with the Goodman and Gerber ,12 mean Composites require mean stress compensation in the fatigue life assessment process;Comparison between the rainflow and frequency domain method shows good combability in the high-cycle fatigue regime N > 103—in this case most of the results are within the scatter area of three;Comparison in the area of low-cycle fatigue regime N < 103 shows that the frequency domain method together with the Goodman model overestimated fatigue results—in this case most results are outside the scatter area of three;Comparison with the use of the Gerber mean stress compensation model shows overall good compatibility between rainflow and frequency calculations. One thing that we can notice is that the calculations with the Gerber model gave results that were over the low-cycle fatigue area;The computation time for the frequency domain method was a fifth of the time in comparison with the rainflow cycle counting method.As we can see, the topic of fatigue lifetime prediction is complex and one of the important factors is definitely the proper mean stress compensation approach. The calculation results will serve the authors in the process of fatigue experiment tests for their own fiber composition for different orientations and prestressed with a similar stress ratio of R = 0.1. The obtained results allowed the authors to formulate some conclusions:


We present a novel modular approach to infer upper bounds on the expected runtimes of probabilistic integer programs automatically. To this end, it computes bounds on the runtimes of program parts and on the sizes of their variables in an alternating way. To evaluate its power, we implemented our approach in a new version of our open-source tool KoAT.


The industry uses subtle tobacco promotion described as ‘below-the-line promotion’, such as handing out free cigarette samples or engaging in tobacco sponsorships4. Given the enormous impact of music on youth lifestyle and identity formation, music events are considered efficient arenas for tobacco promotion and marketing2. In Denmark, the tobacco advertising ban from 2008 is subject to various exemptions, among others allowing for a ‘neutral placement of tobacco’ at point-of-sale5. This exemption is utilised by the tobacco industry to market and promote tobacco. In spite of the ban on sponsorship, the industry provides festivals with funding and free cigarettes for resale, in exchange for exclusive agreements and promotion of tobacco products. A 2010 study of tobacco use at the largest Danish music festival, Roskilde Festival, found that 9% of never-smokers had consumed tobacco for the first time during the festival while 24% of those who had quit smoking, within the past year, relapsed into tobacco use during the festival6. The festival environment thus presents a great risk for youth smoking initiation and relapse.Music festivals and similar arenas are used worldwide by the tobacco industry to promote tobacco to youth and to shape brand image and generate brand recognitionThis article describes the adoption and implementation of tobacco-free initiatives to end tobacco promotion and to denormalise tobacco use at the Danish music festival Strøm.Strøm is an electronic music organization based in Denmark. Strøm aims to stimulate and develop the electronic music scene both in Denmark and internationally through music events, educational activities, workshops and mainly targets children, adolescents and young adults. The largest event is the yearly Strøm Festival in the Copenhagen area. Each year, Strøm activities attract more than 15000 people, mainly adolescents and young adults aged 18–30 years .A 2015 survey of Strøm Festival found that 47% (n=602) of the festival audience had smoked a cigarette on the day or the day before going to the festival, indicating that tobacco played an important role for many of the festival participants .From its establishment in 2007, smoking and tobacco have been an integral part of the visual identity of Strøm. Tobacco products were consistently visible and thus indirectly promoted in social media posts and visual communication material related to the festival. However, in 2014 Strøm decided to cease the indirect promotion and the sale of tobacco products. The decision was based on the role of Strøm as an important facilitator of educational activities for children and youth, which was not ethically compatible with promotion and sale of tobacco. Nonetheless, this was a difficult decision, considering the loss of funding from tobacco sponsorships and concerns about negative feedback from the audience.To consolidate the decision to cease promotion and sale of tobacco among Danish stakeholders, Strøm initiated a partnership with the Danish Cancer Society, the National Institute of Public Health, and The Health and Care Administration of the Municipality of Copenhagen.The aim of the partnership was to denormalise tobacco use and to inspire reflections about the presence of the tobacco industry in the music scene. To reach this goal the partnership focused on three key activities: 1) To create awareness among Strøm staff of the presence of tobacco and their role in indirectly promoting tobacco in the music scene, 2) To end exposure to tobacco marketing and to eliminate tobacco sponsorship in Strøm, and 3) To inspire a wider range of stakeholders in the music industry to reflect upon the relationship between tobacco and music with the hope to expand tobacco-free activities to other music organisations.The initiatives were funded by the Municipality of Copenhagen, while the other partners contributed with specialist knowledge to qualify and share knowledge, since this was the first initiative of its kind. Strøm led the formation and implementation of the initiatives.The first initiative of the tobacco-free strategy consisted of qualitative interviews with employees and volunteers within the Strøm organisation (n=17). Most Strøm staff members also work in other positions in the Danish music scene. In the interviews, examples of direct and indirect tobacco promotion were shown to the respondents and debated subsequently.Using the potential of the interview as an intervention, they aimed to create awareness among the employees and volunteers of the presence of tobacco and smoking in the music scene and to make them reflect on their own experience, attitudes and behaviour to smoking.Several of the Strøm staff members interviewed considered smoking to be a socially accepted and integral part of the music scene and associated it with positive social situations.Interviewees mentioned that they had experienced tobacco marketing at music festivals and at cultural events in general.‘I volunteered in the backstage area at a danish music festival one year, and BAT [British American Tobacco] sponsored all of the area. A few girls were to stand in a bar made of an old minivan and told to smoke or pretend to smoke. We were told that it almost didn’t matter whether we knew the bar menu or not, the pivotal thing was to know everything about their cigarettes and put them on the counter in a certain way when people bought a drink, small subtle triggers like that.’ (Strøm worker)Staff members expressed a clear understanding of the financial dependency on the tobacco industry for music organisations.‘It is no secret that I have received tobacco sponsorships and still receive and sell tobacco at a nightclub that I co-own and at another music event, which I arrange. I also play at music venues, which sell tobacco. Tobacco is a natural part of the food chain; it is not something you think about, it is something you budget for.’ (Strøm worker)A few interviewees noted that the smoking behaviour of performing artists and role models in general is an important factor in the smoking initiation and smoking behaviour of young people.‘When artists smoke while they perform, then I feel like smoking. I take it almost as an invitation to smoke. I attended a concert at [Danish concert-venue] and everyone smoked. It seemed like the security guards gave up trying to stop it.’ (Strøm worker)Most interviewees, however, found that role models from the music scene do not influence their own smoking behaviour or that of young people. They also did not consider their own smoking to have an influence on young people.‘It’s a safe space when you are on the stage and then I smoke if I want to. I don’t give a shit if you are not allowed to smoke. It’s a part of going out and the first thing I think about when I drink a beer.’ (Strøm worker)The partnership developed an official code of conduct to end exposure to tobacco at all Strøm events:There will be no exposure of tobacco products, smoking or any kind of symbol relative to smoking in the press, promotion and communication material developed and distributed by Strøm;Strøm staff members should avoid appearing in Strøm related contexts while smoking;Strøm will not receive any kind of sponsorships from the tobacco industry or tobacco related organisations and;There will be no sale of tobacco products or e-cigarettes at Strøm events.The code was published on the Strøm website and displayed in print at Strøm’s office. After implementing the code, smoking and tobacco products were no longer included in the visual material related to Strøm.Through the Strøm partnership and the various tobacco-free initiatives implemented at Strøm events, the visibility of smoking has significantly decreased in the context of the festival. Through the interviews, it was clear that the Strøm code of conduct has increased awareness among Strøm employees of the potential influence of their smoking behaviour on adolescents.The partnership entailed financial support to develop and run the initiatives. Eliminating the sale of tobacco did not pose a financial constraint to Strøm, which might be due to the festival being less dependent on revenue from tobacco sales as many Strøm events are located in urban spaces where tobacco is available from nearby convenience stores and supermarkets.The third initiative consisted of a survey among stakeholders in the Danish music industry. Stakeholders included bookers, artists, journalists, stakeholders from record companies, industry associations and festivals. In all, 316 persons were contacted and 161 persons (51%) responded to the survey. The aim of the survey was not to gain a fully representative data set but rather to outline the main trends and the potential for adopting further tobacco-free initiatives in the music environment. A secondary objective was to inspire reflection among stakeholders on the relationship between tobacco and music events, while building awareness of the possibility to change existing practices.The survey results suggest positive attitudes towards adopting tobacco-free initiatives to change the norms of tobacco involvement in the music industry. However, the main challenges related to financial sustainability without tobacco industry funding remain substantial.Interviewees reflected on the close links between tobacco and music industry and some questioned the morality of these relations. The stakeholders displayed considerable variation in their will to initiate similar initiatives to those of Strøm. Some would like to continue the initiatives in other parts of the music business, while others found them too radical.Several respondents considered tobacco industry funding a normal and essential part of their business strategies and pointed to the financial challenges associated with leaving behind tobacco industry funding and the concern for a decrease in the alcohol sale following restrictions in the sale of tobacco.Many respondents were, however, very positive or positive (81%) towards the Strøm code of conduct and the initiatives taken to limit exposure of tobacco and smoking.Twenty-four respondents to the survey represent organizations and venues, which could potentially implement tobacco-free initiatives similar to those of Strøm. Of the 24 respondents, 51% expressed that they were very interested or interested to some extent in implementing similar tobacco-free initiatives.The sale of tobacco products and the acceptance of tobacco sponsorships at musical events seemed to be motivated mainly by financial incentives. The respondents feared both financial insecurity without tobacco funding and negative response from the audience following increased focus on tobacco control.On the other hand, the high level of support from music organisations to take on tobacco-free initiatives (51%) points to a potential for expanding the tobacco-free initiatives. Expansion to other organisations would, however, require alternate sources of financing to replace tobacco related income.The Danish music scene is a valued arena for the tobacco industry’s promotion of smoking to young people. In general, there is low awareness among stakeholders in the music industry both of the powerful role of the tobacco industry in its promotion strategies and of their own role in the indirect tobacco promotion to young people. In order to denormalise tobacco in the music scene, a vital first step is to create awareness among the stakeholders. In the Danish musical festival Strøm, a code of conduct to cease indirect tobacco promotion and tobacco sponsorships was a feasible measure towards this goal. To further disseminate the code and denormalise the presence of tobacco in the music scene, it is important to counter both the financial incentives for festivals to promote tobacco and the fear of negative audience response. We have provided an example of how to initiate the denormalisation of tobacco at the music scene and highlighted the importance of raising awareness among artists and other stakeholders from the music scene and the potential for changing the perception of tobacco as an integral part of music culture.


We find that hydrogen charged specimens after plastic deformation display a very characteristic pattern of trailing dipoles and prismatic loops which are absent in uncharged pure metal. We explain these observations by use of a new self consistent kinetic Monte Carlo model, which in fact was initially used to predict the now observed microstructure. The results of this combined theory and experimental study is to shed light on the fundamental mechanism of hydrogen enhanced localised plasticity.Tensile stress relaxation is combined with transmission electron microscopy to reveal dramatic changes in dislocation structure and sub structure in pure  The violent reduction in fracture toughness of steel as a consequence of dissolved hydrogen at the level of some atomic parts per million (appm), at the broadest level of current understanding is either the result of a loss of cohesive strength (the HEDE hypothesis) or the consequence of enhanced localised plasticity (the HELP hypothesis). Other theories such as the role of accumulated vacancy damage or the emission of dislocations from crack surfaces have also been proposed2. One of the striking features of the problem has been a lack of detailed confirmation of observation with theory and modelling; and vice versa. A particular difficulty arises from the putative elastic shielding of dislocation strain fields due to hydrogen. This is well documented both in elegant electron microscopy observations4 and sophisticated theoretical treatments in linear elasticity6. The proposal that HELP is a consequence of elastic shielding by Cottrell atmospheres is untenable in steel because the solubility of hydrogen in body centred cubic α-Fe is about six orders of magnitude too small for the effect to be measurable8. Conversely it has been proposed that the hydrogen trapped locally in the cores of dislocations is responsible for the enhanced plasticity8. Furthermore it is not obvious that hydrogen will increase dislocation mobility under all circumstances. In fact hydrogen may increase or decrease dislocation velocity depending on the conditions of hydrogen concentration, temperature and applied stress in pure α-Fe9.The subject of hydrogen influence on the mechanical behaviour of steel is hugely controversial. On the other hand the dramatic effects of hydrogen on the mechanical integrity of engineering structures is well documentedα-Fe, and we match as closely as possible the experimental and modelling conditions. Furthermore we make contact between our calculations and recently published measurements of activation volume10 and we find a striking accord between experiment and theory. Finally, we conclude with speculations about the role of hydrogen in the generation of dislocation cellular structure which make contact with modern theories of work hardening11.Here, we present for the first time a self consistent kinetic Monte Carlo model that is able to predict average dislocation velocity and to simulate microstructural development that arises from hydrogen self pinning effects. We confirm predictions of the model by transmission electron microscopy (TEM) observations. In both cases we use pure CH,  and either the flow stress or the average dislocation velocity, 13. However, CH, and depending on applied stress and temperature enhanced and reduced depending on the background hydrogen concentration14. In earlier work14, two of us developed an off-lattice kinetic Monte-Carlo method to calculate the velocity of screw dislocations in α-Fe based upon first principles calculations of kink-pair formation energies9. In this model a number of quite serious approximations are made, namely, (i) the kink pair formation energy is affected only by hydrogen ahead of the dislocation in the glide plane; (ii) kink velocity is only affected by hydrogen behind the dislocation in the glide plane; (iii) hydrogen is assumed to remain fixed in place during kink-pair formation and migration; (iv) the time for segments of dislocation to move between Peierls valleys is assumed greater than the hydrogen jump time within the dislocation core. In spite of its simplicity that model was able to predict dislocation velocity as a function of temperature, stress, τ, and nominal hydrogen concentration and it was shown that such a function is non monotonic and that the effect of hydrogen can be to increase or decrease dislocation velocity, depending on conditions; and that the change in velocity compared to pure α-Fe at 300 K and τ = 100 MPa increases by more than a factor of 10 up to 5 appm and then decreases to less than the velocity in pure α-Fe at 20 appm. In addition, the simulations14predicted that under most conditions of hydrogen -loaded α-Fe a moving screw dislocation will leave a trail of debris made up of rows of prismatic loops. The central result of the present paper is that we have found these loops in electron microscope images of deformed, hydrogen-charged α-Fe. On the other hand the model was not able to reproduce activation volume measurements10 which indicate a minimum in the dislocation velocity as a function of hydrogen concentration at about 10 appm at 300 K. We present here a new model which we call “self consistent kinetic Monte-Carlo” (SCkMC) which permits a dynamic non equilibrium distribution of hydrogen about the moving dislocation core. Specific new features of the model are, (i) simultaneous kink nucleation, migration and hydrogen jumping; (ii) kink pair formation energy affected by all hydrogen within the core; (iii) a non equilibrium distribution of hydrogen which depends on temperature and average dislocation velocity; (iv) kink pair formation energy depends on average dislocation velocity; (v) mobile hydrogen during glide—although the total hydrogen occupancy within the core is assumed fixed.At the heart of the simulation of hydrogen effects on plasticity is the model that is used to describe the connection between background, or nominal, hydrogen concentration, 15. We imagine a long dislocation lying in its Peierls valley, a segment of which has migrated towards or into the next Peierls valley so as to make an incipient or complete kink pair. The dislocation is divided into bins of width b, the Burgers vector, along its length and a variable xj is assigned to describe the deviation of the segment lying in the jth bin from the dislocation’s original position in the Peierls valley—the elastic center of the dislocation. There is a periodic Peierls energy landscape described by an energy function, Ep(xj). The energy per unit length of dislocation is then prescribed in the following line tension expression9,The SCkMC is predicated on a parameterised line tension modelK is the associated “spring constant”. The second term is the energy of the segment j depending on its height in the Peierls landscape. The third term, with an implicit sum from 1 to 3 over {pqr}, is the 1-component (perpendicular to [111]) of the Peach–Kohler force arising from a local stress τpq times the displacement of the jth segment of dislocation having a line sense ξ. This term “tilts” the corrugated energy landscape so that the Peierls valley ahead of the dislocation is lower in energy that the one behind, and provides the driving force for glide. The final term expresses the energy associated with a hydrogen atom that is trapped at a position at a distance kth hydrogen atom relative to the elastic centre.The first term describes the energy penalty for two bins which have different amounts of deviation from the original Peierls valley towards the next and 16. Density functional theory (DFT) calculations have identified two core structures of the 17. The HC is very close in configuration to the “saddle point” (SP) core17. DFT calculations furthermore show that hydrogen binds strongly to the EC with three equivalent sites having binding energies of Ei = 256 meV in the so called E1/E2 basin, three in the E3/E4 basin having Ei = 201 meV and six in the E7/E8 basin with Ei = 77 meV9. The strongest binding sites for the HC are one in the H0/H1 basin located at the centre of the core with Ei = 390 meV, and six binding sites denoted H2 having Ei = 189 meV9. As a dislocation moves from EC to HC to EC the E1/E2 traps sites ahead of the dislocation line transform into H0/H1 sites and finally the hydrogen occupies E1/E2 traps sites behind the dislocation line.We first examine the motion of a long straight dislocation, its line moving as a whole. And in the next section we address the actual situation of glide by the Peierls mechanism of kink pair creation and kink migrationχi, of a trap site, i, is determined by the McLean isotherm18,C0 = 10−6CH is the nominal number of hydrogen atoms per Fe atom, and the factor 1/6 accounts for there being six tetrahedral sites per bulk Fe atom. Here, k is the Boltzmann constant and T is the absolute temperature. If we take a sum over all the trap sites in the dislocation core, we will definethis is constant, that is, hydrogen will redistribute dynamically between trap sites during glide but overall the dislocation will not absorb or reject hydrogen; we also only allow hydrogen to redistribute among traps within a plane perpendicular to the dislocation line, in view of the very slow hydrogen pipe diffusivity19. In the case of slow glide, and the maintenance of equilibrium, then as a long straight dislocation moves between two Peierls valleys, we may define the occupation probability, i as20,When the dislocation is lying in its equilibrium Peierls valley the probability of occupancy, x < h, if x describes the position of the dislocation line with respect an origin at the EC elastic centre. As the dislocation glides hydrogen will redistribute between trap sites, which themselves distort and therefore whose trap depth, Ei(x), varies with x. We parameterise Ei(x) by fitting and interpolation of DFT data9. Once that is done, then in association with the line tension model  equilibrium, slow glide in which traps are occupied according to (b) fast glide, in which all hydrogen atoms are fixed in the traps they occupy in the EC initial state before glide.CH = 0 the profile is typical of a calculated Peierls barrier21. The Peierls barrier shown predicted by our model is consistent with the measured estimate of 37 meV/b16. The barrier becomes smaller as CH is increased because hydrogen is stabilising the saddle point core as the E1/E2 traps distort into H0/H1 traps. In fact the effect is strong enough so that when CH exceeds 30 appm the saddle point core is lower in energy than the easy core and their roles are reversed; this is because the total energy gained by hydrogen in deeper traps overwhelms the penalty in core energy. In this way the Peierls barrier is reduced to close to zero and then increases again. However above about 30 appm hydrogen the saddle point is at the EC, and the minimum is in the HC configuration.Figure rapid glide the hydrogen atoms are kept fixed during the movement of a dislocation between Peierls valleys; then as the dislocation moves, hydrogen that was trapped in deep traps may not jump into the newly created traps, but instead remains behind in sites of higher potential energy; hence the Peierls barrier increases continually with CH and the initial and final positions of the dislocation line have not the same energy: the profile is asymmetric as shown in Fig. In the limit of Here 0 < mentclass2pt{minimstabilise the hard core with respect to the easy core, so that hydrogen is able to trigger a core transformation which strongly modifies the Peierls barrier.A highly relevant conclusion is that trapped hydrogen serves to v. Therefore we seek a theory that will predict the profile as a function of v. Because of the finite speed of the dislocation, we expect that the probability of occupancy of trap i, χi(x), differs from its equilibrium value  method26, we may calculate the kink pair formation enthalpy, However Ekp is a function of Ekp: The reason for requiring a entclass1pt{minimah is defined after Eq.  allowinEkp calculated in step 4 is no longer changing to within some tolerance. Figure This process is iterated until Ekp is uniformly small because the applied stress acts to drive a dislocation into the next Peierls valley and this dominates the process of glide. At low stress we observe a large Ekp at low CH, the largest being that of pure α-Fe and zero stress. As CH increases, Ekp decreases, consistent with the calculations shown in Fig. Ekp reaches a minimum at CH ≈ 30 appm in Fig. Ekp is a consequence of the hydrogen-induced core transformation from EC to HC. As CH increases further Ekp rises as a consequence of the increasing Peierls barrier—but now the barrier is at the easy core configuration and the Peierls valley corresponds to the HC.We may interpret Fig. secondary Peierls barrier is low and is not thermally activated. However hydrogen and other interstitials change that. If a hydrogen atom is trapped in the E1/E2 basin just behind the dislocation line and a kink sweeps past, then that hydrogen ends up in a higher enthalpy trap site9, which implies that thermal activation is then required for the kink to proceed. We do not need to rehearse the kMC procedure here since we use the identical scheme as described earlier14. However we should underline the physics here since it is essential in appreciating the present findings. In the case of pure α-Fe, a screw dislocation of typical length of about 1000b will glide as a unit as in face centred cubic metals  since the kink migration speed is so fast that a kink pair has separated to the ends of the dislocation before the next kink pair is activated14. Hence kink collision does not occur. The situation is very different if the kinks suffer solute drag due to hydrogen and other interstitials. A key fact is that kink pairs are created on any one of the three If two kinks on different glide planes collide the resulting defect is an edge jog which is sessile. Our findings earlier14, which we confirm here, are that such jogs amount to self pinning points which drag out edge dipoles and these dipoles will pinch out to create a train of prismatic loop debris, entirely as a consequence of dissolved hydrogen.Glide is a two step process. After the formation of a stable double kink the two kinks will separate in opposite directions. In pure metal, the kink migration or 14. Temperature is 300 K. Rather than using a kink pair formation energy that depends only on stress, CH and temperature; we now employ Ekp as a function of CH is shown in Fig. Conditions of the present self consistent kMC simulations are identical to those of the earlier non self consistent modellingτ < 50 MPa  illustrates the point made earlier that kink velocity is high and the dislocation moves as a straight line .At CH = 10 appm, Fig. Ekp is large . We resolve this apparent contradiction as follows. Since at this hydrogen concentration the Peierls barrier and kink pair formation enthalpy is close to zero, one would expect that α-Fe, the fact that Ekp is nearly vanishing implies that kink pair generation is very rapid on both the primary glide plane and the two cross slip planes. This vastly increases the likelihood of kink collisions on dissimilar slip planes leading to frequent creation of jogs and superjogs, the generation of debris and the subsequent reduction in the average dislocation velocity. Because the thermal activation barrier is small this also reflects on the activation volume which consequently also reached a minium or plateau as seen in Fig. It is notable that the anomaly is associated with a μm. Hydrogen charging was undertaken using standard electrochemical techniques. The stress relaxation test specimens were charged using 1 g/L in an aqueous solution of 3 wt% NaCl and 0.3 wt% NH4 SCN with a current density of 10 mA cm−2 for 48 hours at room temperature. Using thermal desorption spectroscopy we determine the hydrogen concentration to be 30 ± 3 appm. Following charging, samples were immediately subject to repeat stress relaxation tests. Tests were undertaken using a Zwick (BTC T1-FR020 TN A50) universal testing machine. Testing was conducted under displacement control, with a strain rate of 10−5 s−1. A displacement of 0.3 mm was imposed, which gave a stress of 98 MPa in the sample, which was just beyond the yield point of both charged and uncharged specimens. At this point, the strain was held constant for 30 s allowing stress relaxation. Subsequently the specimen was loaded to the same stress of 98 MPa, and then the strain was held constant again for 30 s. The same cycles were repeated until no relaxation was recorded in the relaxation stage. Stress relaxation data was analysed to determine the values of Veff and Vh  observations of the thin foil samples were then conducted in the JEOL F200 TEM operated at an accelerating voltage of 200 kV. Orientation mapping was undertaken in the TEM using a Nanomegas ASTAR system, an automated crystal orientation and phase mapping tool using precession electron diffraction. For mapping, the STEM was in spot size 7, with a 10 micron condenser aperture, a precession angle of 0.7 degrees and a step size of 2.5–10 nm depending on the scan area. Diffraction patterns were recorded using the external camera, with an exposure time of 40 ms.Scanning transmission electron microscopy (STEM) was used to characterise the dislocation structures before and after charging in the unstrained state, and then after stress relaxation tests, again for charged and uncharged specimens. Care was taken to ensure that the observations of dislocation structures from charged and uncharged specimens were, as close as possible, from the same conditions. Samples were assessed using three techniques, namely, high resolution EBSD, precession electron diffraction to determine orientations and TEM. EBSD mapping was used to select grains which had as close as experimentally possible a similar crystal orientation with respect to the stress axis. Imaging of the dislocation structures was undertaken using STEM close to the [111] zone axis. STEM was preferred over TEM for imaging dislocations as it is better able to resolve individual dislocation lines in dense dislocation walls. Specifically, STEM studies can be performed on thicker specimens than in TEM and image contrast from bend contours and thickness fringes are less pronounced due to the convergent probe.et al.10.The dislocation structures in the hydrogen free, strain free samples are as expected, with a low dislocation density, comprising largely homogeneous dislocation distributions. On charging, but without strain, the dislocation density measurably increases, although the total dislocation density remains low. The dislocations tended to be in tangles but individual dislocation lines could still be imaged, Fig. The change in dislocation structure following stress relaxation testing of the hydrogen free pure iron samples is shown in Fig. The dislocation structures for the hydrogen charged stress relaxation samples are markedly different. Dense dislocation tangles are present, Fig. CH and almost returns α-Fe. This is reflected in the measured effective activation volume from Wang et al.10 and plotted in Fig. Veff is seen to rise at about 18 appm, but not quite to reach that of pure α-Fe before falling to a small value associated with enhanced b3, is only a little smaller than the uncharged specimen, 133 b3. This is fully consistent with our calculations which show that α-Fe at the “30 appm anomaly”. At this stage of the work we cannot unequivocally associate our “30 appm anomaly” with the maximum in the activation volume found by Wang et al.10 and plotted in Fig. CH in both the specimens measured by Wang et al.10 and in our simulations. The problem is the same in either case—we are using the amount of hydrogen trapped at defects as a surrogate for the background hydrogen concentration, CH. In Wang et al.’s measurements CH is inferred from the cathodic current density using a number of assumptions on the hydrogen diffusivity and the distribution and depths of traps. It is clear from their method that an uncertainty of about 30 meV in trap depth leads to a factor of 13 as the ratio of the upper and lower estimates of CH. Therefore while they find the anomaly to be at 18 appm, by their own methodology and using reasonable uncertainties in trap depth this may have been as large as 200 appm. The same applies to our assertion that the anomaly occurs at 30 appm. We use the whole range of trap depths in the McLean isotherm to infer the nominal hydrogen concentration that corresponds to a particular simulation. For example the depth of the E2/E3 basin is calculated in DFT to be 256 ± 32 meV9. Given this uncertainty, our assignment of 30 appm of the anomaly is our best estimate of a value that may range between 12 and 105 appm. In spite of this we assert that the “30 appm anomaly” is real  and will have great significance in both the interpretation of experiments and in the establishment of non trivial models for dislocation velocity to be used in multiscale models of hydrogen embrittlement. A key finding here is that the macroscopic measurements that indicate the anomaly can be traced microscopically to the screw dislocation core transformation brought about by hydrogen, Fig. Our calculations of average dislocation velocity as a function of hydrogen concentration, Fig. entclass1pt{minimaα-Fe show that the homogeneous dislocation forest existing in hydrogen free samples transforms into cell walls that separate relatively dislocation free regions. The cell walls can be regarded as dense dislocation tangles. The driving force for cell wall formation arises from the reduction in the total elastic energy of the dislocations due to their clustering. TEM images have shown that the volume of the dislocation free zones and the density of the tangled structures increase with increasing CH in the interval 0–25 appm10. The physics that lies behind dislocation reorganisation due to hydrogen is not yet well understood. It has been commonly accepted that a requirement for cell formation is that dislocations have sufficient mobility out of their slip plane29. Therefore, whether cells form or not depends on factors which determine the ease with which dislocations cross slip or climb. The present SCkMC simulations and experiments show that the probability for formation of kink pairs in secondary slip planes and dislocation segments which glide out of the primary slip plane increases with CH. The angle describing the deviation of the dislocation from the primary slip plane as a function of applied stress and CH is shown in Fig. CH = 30 appm near the EC–HC core transformation, where Ekp is small and kink pair activation is prolific on the cross slip planes. SCkMC simulations show that the dislocation mobility out of the primary slip plane increases significantly for CH > 10 appm and applied stresses higher than 100 MPa. This result of the SCkMC simulations agrees with TEM observations indicating an increase of the density of the tangled structures with increase of hydrogen concentration.Our transmission electron microscopy observations of dislocation structures of both hydrogen charged and uncharged specimens in α-Fe dislocation cell formation is to be expected in some circumstances. We expect (i) that the scale of the cell structure is expected to be smaller as CH is increased; and (ii) that the critical dislocation density at which the transition occurs from uniform distribution to a cell structure decreases as CH is increased. Most experimental evidence on the role of hydrogen on cell formation comes from fatigue testing33. In most of these studies cell formation is found in both uncharged and hydrogen-charged specimens, while there is some evidence that supports our theory that hydrogen serves to decrease the size-scale of the cell structure30. On the other hand, the state of stress and the extent of plasticity are very different under fatigue compared to uniaxial stress relaxation. In addition, our viewpoint is supported by dislocation cell formation observed in stress relaxation testing of uncharged and hydrogen-charged α-Fe34.The appearance of dislocation cell structures and the role of hydrogen is not yet firmly established in the experimental literature. Our own point of view is that we expect that both in uncharged and hydrogen-charged α-Fe. The self consistency arises because of the parametric dependences of the speed on the kink pair formation enthalpy, and the kink pair formation enthalpy on the speed.We demonstrate a new self consistent kinetic Monte Carlo scheme that is able to calculate average dislocation velocity of long straight 14, we find that an effect of hydrogen is to generate large quantities of debris behind a moving screw dislocation, even at room temperature. This is a consequence of kink collisions on different slip planes.As predicted in previous workα-Fe, following tensile stress relaxation testing.The predicted debris has now been found in TEM images of hydrogen loaded CH increases beyond 30 appm and the barrier for glide subsequently appears at the EC state. Signatures of the anomaly are, (i) very frequent kink pair production and creation of self pinning jogs, (ii) a minimum in iii) a plateau, or minimum in the effective activation volume for slip (Fig. We have identified what we call the “30 appm anomaly”. This corresponds to the hydrogen concentration at which there is a core transformation of the screw dislocation from easy core to hard core configuration. At the critical concentration, the Peierls barrier and kink pair formation enthalpy approach close to zero, before increasing as lip Fig. .macroscopic effect is real and is associated with the microscopic phenomenon of a hydrogen-induced screw dislocation core transformation. We have shown that a precise determination of the nominal hydrogen concentration at which the anomaly will occur is problematic both in theory and in experiment. Future work is needed to make a systematic series of stress relaxation experiments in order to make the definitive association of the anomaly with the non monotonic change of activation volumes with hydrogen concentration; and these experiments are planned. It is also a matter of further work to investigate the role of hydrogen and other interstitials such as carbon and nitrogen on the dynamics of cell formation and the development of cellular and sub-grain microstructures in simple uniaxial loading, and to make the connections to observed microstructures under hydrogen-induced fatigue failure.We have identified what we call the “30 appm anomaly” and made contact with published stress relaxation experiments. Our principal conclusion is that this


Koebner phenomenon may be related to frictions of a hearing aid on the external ear and retroauricular skin. Koebner phenomenon may be related to frictions of a hearing aid on the external ear and retroauricular skin. This phenomenon may usually be associated with the development of some skin diseases such as psoriasis, lichen planus, and vasculitis. We report a case of Koebner reaction related to frictions of a hearing aid.Koebner phenomenon is defined as a nonspecific cutaneous stimulus eliciting a disease skin reaction.2A 62‐year‐old man presented in the Department of Otolaryngology—Head and Neck Surgery with a 3‐month history of bilateral retroauricular pruritus. Medical history included presbyacusis and the use of classical hearing aids since 8 years. The patient had a replacement of the hearing aids 3 months ago. Audiologist prescribed a new model with a larger behind‐the‐ear structure Figure . The les3Koebner phenomenon is usually found as new skin lesion located on injured or healthy skin.The main suspected diagnosis of this kind of retroauricular lesion remains the allergic dermatitis. Indeed, a dozen cases of allergic reactions related to hearing aid material have been reported in the literature. The most common allergic molecules are methyl methacrylate and polyethylene glycol, which compose the earplug mold or the behind‐the‐ear material. Therefore, patch test is the main additional examination for the diagnosis. In our patient, we performed a classical patch test, which was negative. A second patch test was realized with scraped behind‐the‐ear material applied to the skin, the result was negative. In the case of a second negative result, a biopsy can be indicated to get a final diagnosis.4The koebnerization of the retroauricular skin related to hearing aids is a very rare cause of dermatitis and one of the main differential diagnoses of contact allergic dermatitis. In both cases, the treatment includes the administration of a corticosteroid ointment. This rare skin reaction may occur at any time of life, and the management needs the collaboration between otolaryngologist and dermatologist to provide an adequate treatment to the patient.The authors have no conflict of interest.JRL: wrote the paper, analyzed the case, conducted literature review, and performed the research. MH and CS: analyzed the case and wrote the part “case report.” MPT: corrected a large part of the paper .