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Promptness and Bounded Fairness in Concurrent and Parameterized Systems

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11990))

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Abstract

We investigate the satisfaction of specifications in Prompt Linear Temporal Logic (\({\text {Prompt-LTL}}\)) by concurrent systems. Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thus adding a quantitative aspect to the specification language. We establish a connection between bounded fairness, bounded stutter equivalence, and the satisfaction of \({\text {Prompt-LTL}} {\setminus }\mathbf{X} \) formulas. Based on this connection, we prove the first cutoff results for different classes of systems with a parametric number of components and quantitative specifications, thereby identifying previously unknown decidable fragments of the parameterized model checking problem.

Partially funded by grant EP/S032207/1 from the Engineering and Physical Sciences Research Council (EPSRC).

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Notes

  1. 1.

    \({\text {Prompt-LTL}}\) can be seen as a fragment of parametric LTL, a logic introduced by Alur et al. [1]. However, since most decision problems for parametric LTL, including model checking, can be reduced to those for \({\text {Prompt-LTL}}\), we can restrict our attention to the simpler logic.

  2. 2.

    By similar arguments as in Emerson and Kahlon [14], our results can be extended to systems with an arbitrary (but fixed) number of process templates. The same holds for open process templates that can receive inputs from an environment, as considered by Außerlechner et al. [5].

  3. 3.

    This restriction has already been considered by Außerlechner et al. [5], and was necessary to support global fairness assumptions.

  4. 4.

    This is only slightly more restrictive than the assumption that they are initializing, as stated in the definition of conjunctive systems in Sect. 3.1.

References

  1. Alur, R., Etessami, K., La Torre, S., Peled, D.A.: Parametric temporal logic for “model measuring”. ACM Trans. Comput. Log. 2(3), 388–407 (2001). https://doi.org/10.1145/377978.377990

    Article  MathSciNet  MATH  Google Scholar 

  2. Aminof, B., Jacobs, S., Khalimov, A., Rubin, S.: Parameterized model checking of token-passing systems. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 262–281. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54013-4_15

    Chapter  MATH  Google Scholar 

  3. Aminof, B., Kotek, T., Rubin, S., Spegni, F., Veith, H.: Parameterized model checking of rendezvous systems. Distrib. Comput. 31(3), 187–222 (2018). https://doi.org/10.1007/s00446-017-0302-6

    Article  MathSciNet  MATH  Google Scholar 

  4. Außerlechner, S., Jacobs, S., Khalimov, A.: Tight cutoffs for guarded protocols with fairness. CoRR abs/1505.03273 (2015). http://arxiv.org/abs/1505.03273

  5. Außerlechner, S., Jacobs, S., Khalimov, A.: Tight cutoffs for guarded protocols with fairness. In: Jobstmann, B., Leino, K.R.M. (eds.) VMCAI 2016. LNCS, vol. 9583, pp. 476–494. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49122-5_23

    Chapter  Google Scholar 

  6. Baier, C., Katoen, J.P.: Principles of Model Checking. vol. 26202649. MIT press Cambridge (2008)

    Google Scholar 

  7. Bloem, R., Jacobs, S., Khalimov, A.: Parameterized synthesis case study: AMBA AHB. In: SYNT. EPTCS, vol. 157, pp. 68–83 (2014). https://doi.org/10.4204/EPTCS.157.9

    Article  MathSciNet  Google Scholar 

  8. Bloem, R., et al.: Decidability of Parameterized Verification. Synthesis Lectures on Distributed Computing Theory, Morgan & Claypool Publishers (2015). https://doi.org/10.2200/S00658ED1V01Y201508DCT013

    Article  Google Scholar 

  9. Bouajjani, A., Jonsson, B., Nilsson, M., Touili, T.: Regular model checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 403–418. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_31

    Chapter  Google Scholar 

  10. Clarke, E., Talupur, M., Touili, T., Veith, H.: Verification by network decomposition. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 276–291. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28644-8_18

    Chapter  Google Scholar 

  11. Clarke, E., Talupur, M., Veith, H.: Proving ptolemy right: the environment abstraction framework for model checking concurrent systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 33–47. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_4

    Chapter  MATH  Google Scholar 

  12. Emerson, E.A., Kahlon, V.: Model checking guarded protocols. In: LICS, pp. 361–370. IEEE Computer Society (2003). https://doi.org/10.1109/LICS.2003.1210076

  13. Emerson, E.A., Namjoshi, K.S.: On reasoning about rings. Found. Comput. Sci. 14(4), 527–549 (2003). https://doi.org/10.1142/S0129054103001881

    Article  MathSciNet  MATH  Google Scholar 

  14. Emerson, E.A., Kahlon, V.: Reducing model checking of the many to the few. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 236–254. Springer, Heidelberg (2000). https://doi.org/10.1007/10721959_19

    Chapter  Google Scholar 

  15. Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS, pp. 352–359. IEEE Computer Society (1999). https://doi.org/10.1109/LICS.1999.782630

  16. Esparza, J.: Keeping a crowd safe: on the complexity of parameterized verification (invited talk). In: STACS. LIPIcs, vol. 25, pp. 1–10. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2014). https://doi.org/10.4230/LIPIcs.STACS.2014.1

  17. Esparza, J., Ganty, P., Majumdar, R.: Parameterized verification of asynchronous shared-memory systems. J. ACM 63(1), 10:1–10:48 (2016). https://doi.org/10.1145/2842603

    Article  MathSciNet  MATH  Google Scholar 

  18. Etessami, K.: Stutter-invariant languages, \(\omega \)-automata, and temporal logic. In: Halbwachs, N., Peled, D. (eds.) CAV 1999. LNCS, vol. 1633, pp. 236–248. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48683-6_22

    Chapter  Google Scholar 

  19. Faymonville, P., Zimmermann, M.: Parametric linear dynamic logic. Inf. Comput. 253, 237–256 (2017). https://doi.org/10.1016/j.ic.2016.07.009

    Article  MathSciNet  MATH  Google Scholar 

  20. German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992). https://doi.org/10.1145/146637.146681

    Article  MathSciNet  MATH  Google Scholar 

  21. Jacobs, S., Bloem, R.: Parameterized synthesis. Log. Methods Comput. Sci. 10, 1–29 (2014). https://doi.org/10.2168/LMCS-10(1:12)2014

    Article  MathSciNet  MATH  Google Scholar 

  22. Jacobs, S., Sakr, M.: Analyzing guarded protocols: better cutoffs, more systems, more expressivity. Verification, Model Checking, and Abstract Interpretation. LNCS, vol. 10747, pp. 247–268. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73721-8_12

    Chapter  Google Scholar 

  23. Jacobs, S., Sakr, M., Zimmermann, M.: Promptness and bounded fairness in concurrent and parameterized systems. CoRR abs/1911.03122 (2019). http://arxiv.org/abs/1911.03122

  24. Jacobs, S., Tentrup, L., Zimmermann, M.: Distributed synthesis for parameterized temporal logics. Inf. Comput. 262, 311–328 (2018). https://doi.org/10.1016/j.ic.2018.09.009

    Article  MathSciNet  MATH  Google Scholar 

  25. Kaiser, A., Kroening, D., Wahl, T.: Dynamic cutoff detection in parameterized concurrent programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 645–659. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14295-6_55

    Chapter  Google Scholar 

  26. Khalimov, A., Jacobs, S., Bloem, R.: Towards efficient parameterized synthesis. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 108–127. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35873-9_9

    Chapter  Google Scholar 

  27. Kupferman, O., Piterman, N., Vardi, M.Y.: From liveness to promptness. Formal Methods Syst. Des. 34(2), 83–103 (2009)

    Article  Google Scholar 

  28. Kurshan, R.P., McMillan, K.L.: A structural induction theorem for processes. Inf. Comput. 117(1), 1–11 (1995). https://doi.org/10.1006/inco.1995.1024

    Article  MathSciNet  MATH  Google Scholar 

  29. Namjoshi, K.S.: Symmetry and completeness in the analysis of parameterized systems. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 299–313. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-69738-1_22

    Chapter  MATH  Google Scholar 

  30. Pnueli, A., Ruah, S., Zuck, L.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45319-9_7

    Chapter  Google Scholar 

  31. Spalazzi, L., Spegni, F.: Parameterized model-checking of timed systems with conjunctive guards. In: Giannakopoulou, D., Kroening, D. (eds.) VSTTE 2014. LNCS, vol. 8471, pp. 235–251. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12154-3_15

    Chapter  Google Scholar 

  32. Spalazzi, L., Spegni, F.: On the existence of cutoffs for model checking disjunctive timed networks. In: CEUR Workshop Proceedings ICTCS/CILC, vol. 1949, pp. 174–185. CEUR-WS.org (2017)

    Google Scholar 

  33. Suzuki, I.: Proving properties of a ring of finite state machines. Inf. Process. Lett. 28(4), 213–214 (1988). https://doi.org/10.1016/0020-0190(88)90211-6

    Article  MathSciNet  MATH  Google Scholar 

  34. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS, pp. 322–331. IEEE Computer Society (1986)

    Google Scholar 

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Authors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Swen Jacobs & Mouhammad Sakr

  2. Saarland University, Saarbrücken, Germany

    Mouhammad Sakr

  3. University of Liverpool, Liverpool, UK

    Martin Zimmermann

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  1. Swen Jacobs
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Correspondence to Swen Jacobs .

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Editors and Affiliations

  1. Ludwig-Maximilians-Universität München, Munich, Germany

    Dirk Beyer

  2. Max Planck Institute for Software Systems, Kaiserslautern, Rheinland-Pfalz, Germany

    Damien Zufferey

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Jacobs, S., Sakr, M., Zimmermann, M. (2020). Promptness and Bounded Fairness in Concurrent and Parameterized Systems. In: Beyer, D., Zufferey, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2020. Lecture Notes in Computer Science(), vol 11990. Springer, Cham. https://doi.org/10.1007/978-3-030-39322-9_16

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  • DOI: https://doi.org/10.1007/978-3-030-39322-9_16

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