Skip to main content

Practical Applications of the Alternating Cycle Decomposition

  • 438 Accesses

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13244)

Abstract

In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., \(\omega \)-automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for \(\omega \)-automata.

Salomon Sickert is supported in part by the Deutsche Forschungsgemeinschaft (DFG) under project number 436811179, and in part funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 787367 (PaVeS)

References

  1. Baarir, S., Duret-Lutz, A.: Mechanizing the minimization of deterministic generalized Büchi automata. In: Proceedings of the 34th IFIP International Conference on Formal Techniques for Distributed Objects, Components and Systems (FORTE’14), Lecture Notes in Computer Science, vol. 8461, pp. 266–283, Springer (Jun 2014), https://doi.org/10.1007/978-3-662-43613-4_17

  2. Babiak, T., Badie, T., Duret-Lutz, A., Křetínský, M., Strejček, J.: Compositional approach to suspension and other improvements to LTL translation. In: Proceedings of the 20th International SPIN Symposium on Model Checking of Software (SPIN’13), Lecture Notes in Computer Science, vol. 7976, pp. 81–98, Springer (Jul 2013), https://doi.org/10.1007/978-3-642-39176-7_6

  3. Babiak, T., Blahoudek, F., Duret-Lutz, A., Klein, J., Křetínský, J., Müller, D., Parker, D., Strejček, J.: The hanoi omega-automata format. In: Kroening, D., Păsăreanu, C.S. (eds.) Computer Aided Verification, pp. 479–486, Springer International Publishing (2015)

    Google Scholar 

  4. Battiti, R., , Protasi, M.: Handbook of Combinatorial Optimization: Volume 1–3, chap. Approximate Algorithms and Heuristics for MAX-SAT, pp. 77–148. Springer US (1998), ISBN 978-1-4613-0303-9, https://doi.org/10.1007/978-1-4613-0303-9_2

  5. Carton, O., Maceiras, R.: Computing the Rabin index of a parity automaton. Informatique théorique et applications 33(6), 495–505 (1999), URL http://www.numdam.org/item/ITA_1999__33_6_495_0/

  6. Casares, A., Colcombet, T., Fijalkow, N.: Optimal transformations of games and automata using Muller conditions. In: Bansal, N., Merelli, E., Worrell, J. (eds.) Proceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP’21), Leibniz International Proceedings in Informatics (LIPIcs), vol. 198, pp. 123:1–123:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany (2021), https://doi.org/10.4230/LIPIcs.ICALP.2021.123

  7. Casares, A., Colcombet, T., Fijalkow, N.: Optimal transformations of muller conditions. Extended version of [6], on ArXiv. (2021), https://arxiv.org/abs/2011.13041

  8. Casares, A., Duret-Lutz, A., Meyer, K.J., Renkin, F., Sickert, S.: Artifact for the paper “Practical applications of the alternating cycle decomposition”. https://doi.org/10.5281/zenodo.5572613 (2021)

  9. Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, E., Xu, L.: Spot 2.0 — a framework for LTL and \(\omega \)-automata manipulation. In: Proceedings of the 14th International Symposium on Automated Technology for Verification and Analysis (ATVA’16), Lecture Notes in Computer Science, vol. 9938, pp. 122–129, Springer (Oct 2016), https://doi.org/10.1007/978-3-319-46520-3_8

  10. Emerson, E.A., Lei, C.L.: Modalities for model checking (extended abstract): Branching time strikes back. In: Proceedings of the 12th ACM symposium on Principles of Programming Languages (POPL’85), pp. 84–96, ACM (1985), https://doi.org/10.1145/318593.318620

  11. Esparza, J., Křetínský, J., Raskin, J.F., Sickert, S.: From LTL and limit-deterministic Büchi automata to deterministic parity automata. In: Proceedings of the 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’17), Lecture Notes in Computer Science, vol. 10205, pp. 426–442, Springer-Verlag (2017), https://doi.org/10.1007/978-3-662-54577-5_25

  12. Esparza, J., Křetínský, J., Sickert, S.: A unified translation of linear temporal logic to \(\omega \)-automata. J. ACM 67(6) (Oct 2020), https://doi.org/10.1145/3417995

  13. Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) Proceedings of the 13th International Conference on Computer Aided Verification (CAV’01), Lecture Notes in Computer Science, vol. 2102, pp. 53–65, Springer-Verlag (2001), https://doi.org/10.1007/3-540-44585-4_6

  14. Giannakopoulou, D., Lerda, F.: From states to transitions: Improving translation of LTL formulæ to Büchi automata. In: Peled, D., Vardi, M. (eds.) Proceedings of the 22nd IFIP WG 6.1 International Conference on Formal Techniques for Networked and Distributed Systems (FORTE’02), Lecture Notes in Computer Science, vol. 2529, pp. 308–326, Springer-Verlag, Houston, Texas (Nov 2002)

    Google Scholar 

  15. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata Logics, and Infinite Games. Springer, Berlin, Heidelberg (2002), https://doi.org/10.1007/3-540-36387-4

  16. Gurevich, Y., Harrington, L.: Trees, automata, and games. In: Proceedings of the 14th annual ACM symposium on Theory of computing (STOC’82), pp. 60–65 (1982), https://doi.org/10.1145/800070.802177

  17. Jacobs, S., Bloem, R., Colange, M., Faymonville, P., Finkbeiner, B., Khalimov, A., Klein, F., Luttenberger, M., Meyer, P.J., Michaud, T., Sakr, M., Sickert, S., Tentrup, L., Walker, A.: The 5th reactive synthesis competition (SYNTCOMP 2018): Benchmarks, participants & results. CoRR abs/1904.07736 (2019), URL http://arxiv.org/abs/1904.07736

  18. Kretínský, J., Meggendorfer, T., Sickert, S.: Owl: A library for \(\omega \)-words, automata, and LTL. In: Proceedings of the 16th International Symposium on Automated Technology for Verification and Analysis (ATVA’18), Lecture Notes in Computer Science, vol. 11138, pp. 543–550, Springer (2018), https://doi.org/10.1007/978-3-030-01090-4_34

  19. Krishnan, Sriram C.and Puri, A., Brayton, R.K.: Deterministic \(\omega \) automata vis-a-vis deterministic buchi automata. In: Algorithms and Computation, pp. 378–386, Springer Berlin Heidelberg, Berlin, Heidelberg (1994)

    Google Scholar 

  20. Křetínský, J., Meggendorfer, T., Waldmann, C., Weininger, M.: Index appearance record for transforming Rabin automata into parity automata. In: Legay, A., Margaria, T. (eds.) Proceedings of the 23st International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’17), Lecture Notes in Computer Science, vol. 10205, pp. 443–460 (2017), https://doi.org/10.1007/978-3-662-54577-5_26

  21. Křetínský, J., Meggendorfer, T., Waldmann, C., Weininger, M.: Index appearance record with preorders. Acta Informatica (2021), https://doi.org/10.1007/s00236-021-00412-y

  22. Löding, C.: Optimal bounds for transformations of \(\omega \)-automata. In: Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’99), Lecture Notes in Computer Science, vol. 1738, pp. 97–109, Springer (1999), https://doi.org/10.1007/3-540-46691-6_8

  23. Luttenberger, M., Meyer, P.J., Sickert, S.: Practical synthesis of reactive systems from LTL specifications via parity games. Acta Informatica pp. 3–36 (2020), https://doi.org/10.1007/s00236-019-00349-3

  24. Löding, C.: Methods for the Transformation of \(\omega \)-Automata: Complexity and Connection to Second Order Logic. Master’s thesis, Institute of Computer Science and Applied Mathematics Christian-Albrechts-University of Kiel (1998), URL https://old.automata.rwth-aachen.de/users/loeding/diploma_loeding.pdf

  25. Meyer, P., Sickert, S.: On the optimal and practical conversion of Emerson-Lei automata into parity automata. Unpublished manuscript, obsoleted by the work of Casares et al. [6]. (2021)

    Google Scholar 

  26. Michaud, T., Colange, M.: Reactive synthesis from LTL specification with Spot. In: Proceedings of the 7th Workshop on Synthesis, SYNT@CAV 2018, Electronic Proceedings in Theoretical Computer Science (2018)

    Google Scholar 

  27. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (POPL’89), pp. 179—190 (1989), https://doi.org/10.1145/75277.75293

  28. Renkin, F., Duret-Lutz, A., Pommellet, A.: Practical “paritizing” of Emerson-Lei automata. In: Proceedings of the 18th International Symposium on Automated Technology for Verification and Analysis (ATVA’20), Lecture Notes in Computer Science, vol. 12302, pp. 127–143, Springer (Oct 2020), https://doi.org/10.1007/978-3-030-59152-6_7

  29. Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Logics for Concurrency: Structure versus Automata, volume 1043 of Lecture Notes in Computer Science, pp. 238–266, Springer-Verlag (1996)

    Google Scholar 

  30. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proceedings of the 1st Symposium on Logic in Computer Science (LICS’86), pp. 332–344, IEEE Computer Society Press (Jun 1986)

    Google Scholar 

  31. Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200(1), 135–183 (1998), https://doi.org/10.1016/S0304-3975(98)00009-7

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antonio Casares .

Editor information

Editors and Affiliations

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2022 The Author(s)

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Casares, A., Duret-Lutz, A., Meyer, K.J., Renkin, F., Sickert, S. (2022). Practical Applications of the Alternating Cycle Decomposition. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13244. Springer, Cham. https://doi.org/10.1007/978-3-030-99527-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-99527-0_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-99526-3

  • Online ISBN: 978-3-030-99527-0

  • eBook Packages: Computer ScienceComputer Science (R0)