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Link to original content: https://doi.org/10.1007/978-3-642-24364-6_6
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The Complexity of Reversal-Bounded Model-Checking

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Frontiers of Combining Systems (FroCoS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6989))

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Abstract

We study model-checking problems on counter systems when guards are quantifier-free Presburger formulae, the specification languages are LTL-like dialects with arithmetical constraints and the runs are restricted to reversal-bounded ones. We introduce a generalization of reversal-boundedness and we show the NExpTime-completeness of the reversal-bounded model-checking problem as well as for related reversalbounded reachability problems. As a by-product, we show the effective Presburger definability for sets of configurations for which there is a reversal-bounded run verifying a given temporal formula. Our results generalize existing results about reversal-bounded counter automata and provides a uniform and more general framework.

Work supported by Agence Nationale de la Recherche, grant ANR-06-SETIN-001 and by the European Commission, Project 227977-SMScom.

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References

  1. Alur, R., Henzinger, T.: A really temporal logic. In: FOCS 1989, pp. 164–169. IEEE, Los Alamitos (1989)

    Google Scholar 

  2. Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Becker, B., Dax, C., Eisinger, J., Klaedtke, F.: LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 307–310. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Bersani, M., Demri, S.: The complexity of reversal-bounded model checking. Tech. Rep. LSV-11-10, LSV, ENS Cachan, France (May 2011)

    Google Scholar 

  5. Bersani, M., Frigeri, A., Morzenti, A., Pradella, M., Rossi, M., San Pietro, P.: Bounded reachability for temporal logic over constraint systems. In: TIME 2010, pp. 43–50. IEEE, Los Alamitos (2010)

    Google Scholar 

  6. Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58, 118–149 (2003)

    Google Scholar 

  7. Borosh, I., Treybig, L.: Bounds on positive integral solutions of linear diophantine equations. Proocedings of The American Mathematical Society 55, 299–304 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bouajjani, A., Echahed, R., Habermehl, P.: On the verification problem of nonregular properties for nonregular processes. In: LICS 1995, pp. 123–133 (1995)

    Google Scholar 

  9. Čerāns, K.: Deciding properties of integral relational automata. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 35–46. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  10. Dang, Z., Ibarra, O., San Pietro, P.: Liveness verification of reversal-bounded multicounter machines with a free counter. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 132–143. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Demri, S.: On Selective Unboundedness of VASS. In: INFINITY 2010. EPTCS, vol. 39, pp. 1–15 (2010)

    Google Scholar 

  12. Esparza, J.: Decidability and complexity of Petri net problems — an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)

    Chapter  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)

    Chapter  Google Scholar 

  14. Gurari, E., Ibarra, O.: The complexity of decision problems for finite-turn multicounter machines. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 495–505. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  15. Habermehl, P.: On the complexity of the linear-time mu-calculus for Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 102–116. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  16. Hague, M., Lin, A.W.: Model checking recursive programs with numeric data types. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 743–759. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Howell, R., Rosier, L.: An analysis of the nonemptiness problem for classes of reversal-bounded multicounter machines. JCSS 34(1), 55–74 (1987)

    MATH  MathSciNet  Google Scholar 

  18. Ibarra, O.H., Bultan, T., Su, J.: Reachability analysis for some models of infinite-state transition systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 183–198. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Ibarra, O., Su, J., Dang, Z., Bultan, T., Kemmerer, R.: Counter Machines and Verification Problems. TCS 289(1), 165–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  21. Kopczynski, E., To, A.: Parikh Images of Grammars: Complexity and Applications. In: LICS 2010, pp. 80–89. IEEE, Los Alamitos (2010)

    Google Scholar 

  22. Laroussinie, F., Meyer, A., Petonnet, E.: Counting LTL. In: TIME 2010, pp. 51–58. IEEE, Los Alamitos (2010)

    Google Scholar 

  23. Leroux, J., Point, G.: TaPAS: The Talence Presburger Arithmetic Suite. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 182–185. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  24. Leroux, J., Sutre, G.: Flat counter automata almost everywhere! In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 489–503. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Lutz, C.: NEXPTIME-complete description logics with concrete domains. ACM ToCL 5(4), 669–705 (2004)

    Article  MathSciNet  Google Scholar 

  26. de Moura, L., Björner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Papadimitriou, C.: On the complexity of integer programming. JACM 28(4), 765–768 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  28. Presburger, M.: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: Comptes Rendus du premier congrès de mathématiciens des Pays Slaves, Warszawa, pp. 92–101 (1930)

    Google Scholar 

  29. Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  30. Rackoff, C.: The covering and boundedness problems for vector addition systems. TCS 6(2), 223–231 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  31. Suzuki, N., Jefferson, D.: Verification Decidability of Presburger Array Programs. JACM 27(1), 191–205 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  32. To, A.: Model Checking Infinite-State Systems: Generic and Specific Approaches. Ph.D. thesis, School of Informatics, University of Edinburgh (2010)

    Google Scholar 

  33. To, A., Libkin, L.: Algorithmic metatheorems for decidable LTL model checking over infinite systems. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 221–236. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  34. Vardi, M., Wolper, P.: Reasoning about infinite computations. I&C 115, 1–37 (1994)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS, INRIA, France

    Marcello M. Bersani & Stéphane Demri

  2. Politecnico di Milano, Italy

    Marcello M. Bersani

Authors
  1. Marcello M. Bersani
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  2. Stéphane Demri
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Editor information

Editors and Affiliations

  1. University of Iowa, USA

    Cesare Tinelli

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

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Bersani, M.M., Demri, S. (2011). The Complexity of Reversal-Bounded Model-Checking. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-24364-6_6

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