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A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8902))

Abstract

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investigate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods.

Research partially funded by projects EU ASCENS (nr. 257414), EU QUANTICOL (nr. 600708), IT MIUR CINA and PAR FAS 2007-2013 Regione Toscana TRACE-IT.

An extended version containing full proofs is available at [1]

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References

  1. Ciancia, V., Sammartino, M.: A class of automata for the verification of infinite, resource-allocating behaviours - extended version. CoRR abs/1310.3945 (2014)

    Google Scholar 

  2. Clarke, E.M., Schlingloff, B.H.: Model checking. In: Handbook of Automated Reasoning, pp. 1635–1790. Elsevier (2001)

    Google Scholar 

  3. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundl. Math. 6, 66–92 (1960)

    Article  MATH  Google Scholar 

  4. Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc. 98, 21–51 (1961)

    Article  MathSciNet  Google Scholar 

  5. Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes. I/II. Inf. Comput. 100(1), 1–77 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fiore, M.P., Turi, D.: Semantics of name and value passing. In: LICS 2001, pp. 93–104. IEEE Computer Society (2001)

    Google Scholar 

  7. Bonchi, F., Buscemi, M.G., Ciancia, V., Gadducci, F.: A presheaf environment for the explicit fusion calculus. J. Autom. Reasoning 49(2), 161–183 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Miculan, M.: A categorical model of the fusion calculus. Electr. Not. Theor. Comp. Sci. 218, 275–293 (2008)

    Article  Google Scholar 

  9. Ghani, N., Yemane, K., Victor, B.: Relationally staged computations in calculi of mobile processes. Electr. Not. Theor. Comp. Sci. 106, 105–120 (2004)

    Article  MathSciNet  Google Scholar 

  10. Montanari, U., Sammartino, M.: A network-conscious \(\pi \)-calculus and its coalgebraic semantics. Theor. Comput. Sci. 546, 188–224 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  11. Montanari, U., Pistore, M.: Structured coalgebras and minimal hd-automata for the \(\pi \)-calculus. Theor. Comput. Sci. 340(3), 539–576 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Bojanczyk, M., Klin, B., Lasota, S.: Automata with group actions. In: LICS 2011, pp. 355–364. IEEE Computer Society (2011)

    Google Scholar 

  13. Gadducci, F., Miculan, M., Montanari, U.: About permutation algebras, (pre)sheaves and named sets. Higher-Ord. Symb. Comp. 19(2–3), 283–304 (2006)

    Article  MATH  Google Scholar 

  14. Fiore, M.P., Staton, S.: Comparing operational models of name-passing process calculi. Inf. Comput. 204(4), 524–560 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ciancia, V., Kurz, A., Montanari, U.: Families of symmetries as efficient models of resource binding. Electr. Not. Theor. Comp. Sci. 264(2), 63–81 (2010)

    Article  MathSciNet  Google Scholar 

  16. Ciancia, V., Montanari, U.: Symmetries, local names and dynamic (de)-allocation of names. Inf. Comput. 208(12), 1349–1367 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  17. Tzevelekos, N.: Fresh-register automata. In: POPL 2011, pp. 295–306. ACM (2011)

    Google Scholar 

  18. Kurz, A., Suzuki, T., Tuosto, E.: On nominal regular languages with binders. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 255–269. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Gabbay, M.J., Ciancia, V.: Freshness and name-restriction in sets of traces with names. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 365–380. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Maler, O., Pnueli, A.: On the learnability of infinitary regular sets. Inf. Comput. 118(2), 316–326 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  21. Farzan, A., Chen, Y.-F., Clarke, E.M., Tsay, Y.-K., Wang, B.-Y.: Extending automated compositional verification to the full class of omega-regular languages. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 2–17. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Ciancia, V., Venema, Y.: Stream automata are coalgebras. In: Pattinson, D., Schröder, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 90–108. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Gabbay, M., Pitts, A.M.: A new approach to abstract syntax with variable binding. Formal Asp. Comput. 13(3–5), 341–363 (2002)

    Article  MATH  Google Scholar 

  24. Pistore, M.: History Dependent Automata. PhD thesis, University of Pisa (1999)

    Google Scholar 

  25. Calbrix, H., Nivat, M., Podelski, A.: Ultimately periodic words of rational w-languages. In: Main, M.G., Melton, A.C., Mislove, M.W., Schmidt, D., Brookes, S.D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 554–556. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  26. Büchi, J.R.: On a decision method in restricted second order arithmetic. In: 1960 International Congress on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1962)

    Google Scholar 

  27. Bengtson, J., Johansson, M., Parrow, J., Victor, B.: Psi-calculi: a framework for mobile processes with nominal data and logic. LMCS 7(1) (2011)

    Google Scholar 

  28. Bojańczyk, M.: Modelling infinite structures with atoms. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds.) WoLLIC 2013. LNCS, vol. 8071, pp. 13–28. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  29. Väänänen, J.A.: Dependence Logic - A New Approach to Independence Friendly Logic. London Mathematical Society student texts, vol. 70. Cambridge University Press (2007)

    Google Scholar 

  30. Galliani, P.: The Dynamics of Imperfect Information. PhD thesis, University of Amsterdam (September 2012)

    Google Scholar 

  31. Demri, S., Lazic, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3) (2009)

    Google Scholar 

  32. Lazic, R.: Safety alternating automata on data words. ACM Trans. Comput. Log. 12(2), 10 (2011)

    Article  MathSciNet  Google Scholar 

  33. Bojanczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Log. 12(4), 27 (2011)

    Article  MathSciNet  Google Scholar 

  34. Kara, A., Schwentick, T., Tan, T.: Feasible automata for two-variable logic with successor on data words. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 351–362. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  35. Bollig, B.: An automaton over data words that captures emso logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 171–186. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  36. Kara, A., Tan, T.: Extending Büchi automata with constraints on data values. CoRR abs/1012.5439 (2010)

    Google Scholar 

  37. Grumberg, O., Kupferman, O., Sheinvald, S.: Variable automata over infinite alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

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Correspondence to Vincenzo Ciancia or Matteo Sammartino .

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Ciancia, V., Sammartino, M. (2014). A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours. In: Maffei, M., Tuosto, E. (eds) Trustworthy Global Computing. TGC 2014. Lecture Notes in Computer Science(), vol 8902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45917-1_7

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  • DOI: https://doi.org/10.1007/978-3-662-45917-1_7

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