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Weakly Synchronous Systems with Three Machines Are Turing Powerful

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Reachability Problems (RP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14235))

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Abstract

Communicating finite-state machines (CFMs) are a Turing powerful model of asynchronous message-passing distributed systems. In weakly synchronous systems, processes communicate through phases in which messages are first sent and then received, for each process. Such systems enjoy a limited form of synchronization, and for some communication models, this restriction is enough to make the reachability problem decidable. In particular, we explore the intriguing case of p2p (FIFO) communication, for which the reachability problem is known to be undecidable for four processes, but decidable for two. We show that the configuration reachability problem for weakly synchronous systems of three processes is undecidable. This result is heavily inspired by our study on the treewidth of the Message Sequence Charts (MSCs) that might be generated by such systems. In this sense, the main contribution of this work is a weakly synchronous system with three processes that generates MSCs of arbitrarily large treewidth.

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Notes

  1. 1.

    We do not explicitly use tree-decompositions, we refer to [4] for their formal definitions.

References

  1. Akroun, L., Salaün, G.: Automated verification of automata communicating via FIFO and bag buffers. Formal Methods Syst. Des. 52(3), 260–276 (2018). https://doi.org/10.1007/s10703-017-0285-8

  2. Basu, S., Bultan, T.: Choreography conformance via synchronizability. In: Srinivasan, S., Ramamritham, K., Kumar, A., Ravindra, M.P., Bertino, E., Kumar, R. (eds.) Proceedings of the 20th International Conference on World Wide Web, WWW 2011, Hyderabad, India, March 28–April 1, 2011, pp. 795–804. ACM (2011)

    Google Scholar 

  3. Basu, S., Bultan, T.: On deciding synchronizability for asynchronously communicating systems. Theor. Comput. Sci. 656, 60–75 (2016). https://doi.org/10.1016/j.tcs.2016.09.023

  4. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209(1–2), 1–45 (1998). https://doi.org/10.1016/S0304-3975(97)00228-4

  5. Bollig, B., Di Giusto, C., Finkel, A., Laversa, L., Lozes, É., Suresh, A.: A unifying framework for deciding synchronizability. In: Haddad, S., Varacca, D. (eds.) 32nd International Conference on Concurrency Theory, CONCUR 2021, August 24–27, 2021. LIPIcs, vol. 203, pp. 14:1–14:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Virtual Conference (2021). https://doi.org/10.4230/LIPIcs.CONCUR.2021.14

  6. Bollig, B., Di Giusto, C., Finkel, A., Laversa, L., Lozes, É., Suresh, A.: A unifying framework for deciding synchronizability (extended version). Technical report (2021). https://hal.archives-ouvertes.fr/hal-03278370/document

  7. Bouajjani, A., Enea, C., Ji, K., Qadeer, S.: On the completeness of verifying message passing programs under bounded asynchrony. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10982, pp. 372–391. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96142-2_23

    Chapter  Google Scholar 

  8. Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30(2), 323–342 (1983). https://doi.org/10.1145/322374.322380

  9. Charron-Bost, B., Mattern, F., Tel, G.: Synchronous, asynchronous, and causally ordered communication. Distributed Comput. 9(4), 173–191 (1996). https://doi.org/10.1007/s004460050018

  10. Di Giusto, C., Ferré, D., Laversa, L., Lozes, É.: A partial order view of message-passing communication models. Proc. ACM Program. Lang. 7(POPL), 1601–1627 (2023). https://doi.org/10.1145/3571248

  11. Di Giusto, C., Ferré, D., Lozes, E., Nisse, N.: Weakly synchronous systems with three machines are Turing powerful. Technical report, Université Côte d’Azur, CNRS, I3S, France; Université Côte d’Azur, Inria, CNRS, I3S, France (2023). https://hal.science/hal-04182953

  12. Finkel, A., Lozes, É.: Synchronizability of communicating finite state machines is not decidable. In: Chatzigiannakis, I., Indyk, P., Kuhn, F., Muscholl, A. (eds.) 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10–14, 2017, Warsaw, Poland. LIPIcs, vol. 80, pp. 122:1–122:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

    Google Scholar 

  13. Finkel, A., Sangnier, A.: Reversal-bounded counter machines revisited. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 323–334. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85238-4_26

    Chapter  Google Scholar 

  14. Genest, B., Kuske, D., Muscholl, A.: On communicating automata with bounded channels. Fundam. Informaticae 80(1-3), 147–167 (2007). http://content.iospress.com/articles/fundamenta-informaticae/fi80-1-3-09

  15. Heußner, A., Leroux, J., Muscholl, A., Sutre, G.: Reachability analysis of communicating pushdown systems. In: Ong, L. (ed.) FoSSaCS 2010. LNCS, vol. 6014, pp. 267–281. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12032-9_19

    Chapter  MATH  Google Scholar 

  16. Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. ACM (JACM) 25(1), 116–133 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  17. ITU-T: Recommendation ITU-T Z.120: Message sequence chart (MSC). Technical report, International Telecommunication Union, Geneva (2011)

    Google Scholar 

  18. Lohrey, M., Muscholl, A.: Bounded MSC communication. In: Nielsen, M., Engberg, U. (eds.) FoSSaCS 2002. LNCS, vol. 2303, pp. 295–309. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45931-6_21

    Chapter  Google Scholar 

  19. Mayr, E.W.: An algorithm for the general petri net reachability problem. In: Symposium on the Theory of Computing (1981)

    Google Scholar 

  20. Torre, S.L., Madhusudan, P., Parlato, G.: Context-bounded analysis of concurrent queue systems. In: Tools and Algorithms for the Construction and Analysis of Systems, 14th International Conference, TACAS 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29–April 6, 2008. Proceedings, pp. 299–314 (2008). https://doi.org/10.1007/978-3-540-78800-3_21

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Authors and Affiliations

  1. Université Côte d’Azur, CNRS, I3S, Nice, France

    Cinzia Di Giusto & Etienne Lozes

  2. Université Côte d’Azur, Inria, CNRS, I3S, Nice, France

    Davide Ferre’ & Nicolas Nisse

Authors
  1. Cinzia Di Giusto
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  2. Davide Ferre’
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  3. Etienne Lozes
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  4. Nicolas Nisse
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Corresponding author

Correspondence to Cinzia Di Giusto .

Editor information

Editors and Affiliations

  1. École Polytechnique, Paris, France

    Olivier Bournez

  2. Université Côte d’Azur, Nice, France

    Enrico Formenti

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Di Giusto, C., Ferre’, D., Lozes, E., Nisse, N. (2023). Weakly Synchronous Systems with Three Machines Are Turing Powerful. In: Bournez, O., Formenti, E., Potapov, I. (eds) Reachability Problems. RP 2023. Lecture Notes in Computer Science, vol 14235. Springer, Cham. https://doi.org/10.1007/978-3-031-45286-4_3

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  • DOI: https://doi.org/10.1007/978-3-031-45286-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45285-7

  • Online ISBN: 978-3-031-45286-4

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