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Bounded satisfiability checking of metric temporal logic specifications

Published:30 July 2013Publication History
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Abstract

We introduce bounded satisfiability checking, a verification technique that extends bounded model checking by allowing also the analysis of a descriptive model, consisting of temporal logic formulae, instead of the more customary operational model, consisting of a state transition system. We define techniques for encoding temporal logic formulae into Boolean logic that support the use of bi-infinite time domain and of metric time operators. In the framework of bounded satisfiability checking, we show how a descriptive model can be refined into an operational one, and how the correctness of such a refinement can be verified for the bounded case, setting the stage for a stepwise system development method based on a bounded model refinement. Finally, we show how the adoption of a modular approach can make the bounded refinement process more manageable and efficient. All introduced concepts are extensively applied to a set of case studies, and thoroughly experimented through Zot, our SAT solver-based verification toolset.

References

  1. Abrial, J.-R. 1996. The B-Book: Assigning Programs to Meanings. Cambridge University Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bengtsson, J., Larsen, K. G., Larsson, F., Pettersson, P., and Yi, W. 1995. UPPAAL: A tool suite for automatic verification of real--time systems. In Proceedings of the Workshop on Verification and Control of Hybrid Systems III. Lecture Notes in Computer Science, vol. 1066, Springer, 232--243. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Bersani, M. M., Furia, C. A., Pradella, M., and Rossi, M. 2009. Integrated modeling and verification of real-time systems through multiple paradigms. In Proceedings of the 7th IEEE International Conference on Software Engineering and Formal Methods (SEFM'09). D. V. Hung and P. Krishnan, Eds., IEEE Computer Society, 13--22. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Biere, A., Cimatti, A., Clarke, E., and Zhu, Y. 1999. Symbolic model checking without bdds. In Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems. Lecture Notes in Computer Science, vol. 1579, Springer, 193--207. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Biere, A., Heljanko, K., Junttila, T., Latvala, T., and Schuppan, V. 2006. Linear encodings of bounded ltl model checking. Logic. Methods Comput. Sci. 2, 5, 1--64.Google ScholarGoogle ScholarCross RefCross Ref
  6. Ciapessoni, E., Mirandola, P., Coen-Porisini, A., Mandrioli, D., and Morzenti, A. 1999. From formal models to formally based methods: An industrial experience. ACM Trans. Softw. Eng. Methodol. 8, 1, 79--113. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Cimatti, A., Clarke, E. M., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., and Tacchella, A. 2002. NuSMV 2: An opensource tool for symbolic model checking. In Proceedings of the 14th International Conference on Computer Aided Verification (CAV'02). Springer, 359--364. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Clarke, E., Kroening, D., and Lerda, F. 2004. A tool for checking ansi-c programs. In Proceedings of the 10th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'04). K. Jensen and A. Podelski, Eds, Lecture Notes in Computer Science, vol. 2988, Springer, 168--176.Google ScholarGoogle Scholar
  9. Clarke, E., Kroening, D., Ouaknine, J., and Strichman, O. 2005. Computational challenges in bounded model checking. Softw. Tools Technol. Transfer 7, 2, 174--183.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Clarke, E. M., Gupta, A., Kukula, J. H., and Strichman, O. 2002. SAT based abstraction-refinement using ilp and machine learning techniques. In Proceedings of the 14th International Conference on Computer Aided Verification (CAV'02). E. Brinksma and K. G. Larsen, Eds., Lecture Notes in Computer Science, vol. 2404, Springer, 265--279. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Coen-Porisini, A., Pradella, M., and San Pietro, P. 1998. A finite-domain semantics for testing temporal logic specifications. In Proceedings of the 5th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems (FTRTFT'98). 41--54. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. De Moura, L. M., Owre, S., Ruess, H., Rushby, J. M., Shankar, N., Sorea, M., and Tiwari, A. 2004. SAL 2. In Proceedings of the 16th International Conference on Computer Aided Verification (CAV'04). R. Alur and D. Peled, Eds., Lecture Notes in Computer Science, vol. 3114., Springer, 496--500.Google ScholarGoogle Scholar
  13. De Roever, W. P. 1997. The need for compositional proof systems: A survey. In Proceedings of the International Symposium on Compositionality: The Significant Difference (COMPOS'97). W. P. de Roever, H. Langmaack, and A. Pnueli, Eds., Lecture Notes in Computer Science, vol. 1536, Springer, 1--22. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. De Roever, W.-P., De Boer, F., Hannemann, U., Hooman, J., Lakhnech, Y., Poel, M., and Zwiers, J. 2001. Concurrency Verification: Introduction to Compositional and Noncompositional Methods. Cambridge University Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Een, N. and Sorensson, N. 2003. An extensible sat-solver. In Proceedings of the 6th International Conference on Theory and Application of Satisfiability Testing (SAT'03). Lecture Notes in Computer Science, vol. 2919, Springer, 502--518.Google ScholarGoogle ScholarCross RefCross Ref
  16. Felder, M. and Morzenti, A. 1994. Validating real-time systems by history-checking trio specifications. ACM Trans. Softw. Eng. Methodol. 3, 4, 308--339. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Furia, C. A., Pradella, M., and Rossi, M. 2008a. Automated verification of dense-time mtl specifications via discretetime approximation. In Proceedings of the 15th International Symposium on Formal Methods (FM'08). J. Cuellar, T. S. E. Maibaum, and K. Sere, Eds., Lecture Notes in Computer Science, vol. 5014, Springer, 132--147. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Furia, C. A., Pradella, M., and Rossi, M. 2008b. Practical automated partial verification of multi-paradigm real-time models. In Proceedings of the 10th International Conference on Formal Methods and Software Engineering (ICFEM'08). S. Liu, T. S. E. Maibaum, and K. Araki, Eds., Lecture Notes in Computer Science, vol. 5256, Springer, 298--317. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Furia, C. A., Rossi, M., Mandrioli, D., and Morzenti, A. 2007. Automated compositional proofs for real-time systems. Theor. Comput. Sci. 376, 3, 164--184. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Gargantini, A. and Morzenti, A. 2001. Automated deductive requirements analysis of critical systems. ACM Trans. Softw. Eng. Methodol. 10, 3, 255--307. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Ghezzi, C., Mandrioli, D., and Morzenti, A. 1990. TRIO: A logic language for executable specifications of real-time systems. J. Syst. Softw. 12, 2, 107--123. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Gire, F. and Nivat, M. 1991. Langages algebriques de mots biinfinis. Theor. Comput. Sci. 86, 2, 277--323. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Grumberg, O. and Long, D. E. 1994. Model checking and modular verification. ACM Trans. Program. Lang. Syst. 16, 3, 843--871. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Heitmeyer, C. and Mandrioli, D. 1996. Formal Methods for Real-Time Computing. John Wiley and Sons, New York. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Heljanko, K., Junttila, T. A., and Latvala, T. 2005. Incremental and complete bounded model checking for full pltl. In Proceedings of the 17th International Conference on Computer Aided Verification (CAV'05). K. Etessami and S. K. Rajamani, Eds., Lecture Notes in Computer Science, vol. 3576, Springer, 98--111. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Holzmann, G. J. 1997. The model checker spin. IEEE Trans. Softw. Engin. 23, 5, 279--295. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Hooman, J. 1998. Compositional verification of real-time applications. In Revised Lectures from the International Symposium on Compositionality: The Significant Difference (COMPOS'97). Lecture Notes in Computer Science, vol. 1536, Springer, 276--300. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Jackson, D. 2003. Alloy: A logical modelling language. In Proceedings of the 3rd International Conference on Formal Specification and Development in Z and B, D. Bert, J. P. Bowen, S. King, and M. A. Walden, Eds. Lecture Notes in Computer Science, vol. 2651, Springer, 1. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Jhala, R. and Mcmillan, K. L. 2001. Microarchitecture verification by compositional model checking. In Proceedings of the 13th International Conference on Computer Aided Verification (CAV'01), G. Berry, H. Comon, and A. Finkel, Eds. Lecture Notes in Computer Science, vol. 2102. Springer, 396--410. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Kamp, J. A. W. 1968. Tense logic and the theory of linear order. Ph.D. thesis. University of California at Los Angeles.Google ScholarGoogle Scholar
  31. Koymans, R. 1990. Specifying real-time properties with metric temporal logic. Real-Time Syst. 2, 4, 255--299. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Kroening, D. and Strichman, O. 2003. Efficient computation of recurrence diameters. In Proceedings of the 4th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI'03), L. D. Zuck, P. C. Attie, A. Cortesi, and S. Mukhopadhyay, Eds. Lecture Notes in Computer Science, vol. 2575. Springer, 298--309. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Lamport, L. 1987. A fast mutual exclusion algorithm. ACM Trans. Comput. Syst. 5, 1, 1--11. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Lewis, M., Schubert, T., and Becker., B. 2007. Multithreaded sat solving. In 12th Asia and South Pacific Design Automation Conference. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Lichtenstein, O., Pnueli, A., and Zuck, L. D. 1985. The glory of the past. In Proceedings of the Conference on Logic of Programs. Springer, 196--218. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Mandrioli, D., Morasca, S., and Morzenti, A. 1995. Generating test cases for real-time systems from logic specifications. ACM Trans. Comput. Syst. 13, 4, 365--398. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Manolios, P., Srinivasan, S. K., and Vroon, D. 2007. BAT: The bit-level analysis tool. In Proceedings of the 19th International Conference on Computer Aided Verification (CAV'07), W. Damm and H. Hermanns, Eds. Lecture Notes in Computer Science, vol. 4590. Springer, 303--306. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Mcmillan, K. L. 2000. A methodology for hardware verification using compositional model checking. Sci. Comput. Program. 37, 1--3, 279--309. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Morasca, S., Morzenti, A., and San Pietro, P. 2000. A case study on applying a tool for automated system analysis object oriented logic specification of time-critical systems. based on modular specifications written in trio. Autom. Softw. Engin. 7, 2, 125--155. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Morzenti, A., Mandrioli, D., and Ghezzi, C. 1992. A model parametric real-time logic. ACM Trans. Program. Lang. Syst. 14, 4, 521--573. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Morzenti, A., Pradella, M., San Pietro, P., and Spoletini, P. 2003. Model-checking trio specifications in spin. In Proceedings of the International Symposium of Formal Methods Europe (FME'03). K. Araki, S. Gnesi, and D. Mandrioli, Eds., Lecture Notes in Computer Science, vol. 2805, Springer, 542--561.Google ScholarGoogle Scholar
  42. Morzenti, A. and San Pietro, P. 1994. Object-oriented logical specification of time-critical systems. ACM Trans. Softw. Engin. Methodol. 3, 1, 56--98. Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Nieuwenhuis, R., Oliveras, A., and Tinelli, C. 2006. Solving sat and sat modulo theories: From an abstract davis--Putnam--Logemann--Loveland procedure to dpll(t). J. ACM 53, 6, 937--977. Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Ostroff, J. S. 1999. Composition and refinement of discrte real-time systems. ACM Trans. Softw. Engin. Methodol. 8, 1, 1--48. Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Perrin, D. and Pin, J.-E. 2004. Infinite Words. Automata, Semigroups, Logic and Games. Pure and Applied Mathematics, vol. 141, Elsevier.Google ScholarGoogle Scholar
  46. Pnueli, A. 1977. The temporal logic of programs. In Proceedings of the 18th IEEE Symposium on the Foundations of Computer Science (FOCS'77). IEEE Computer Society, 46--57. Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. Pradella, M., Morzenti, A., and San Pietro, P. 2007. The symmetry of the past and of the future: Bi-infinite time in the verification of temporal properties. In Proceedings of the 6th Joint Meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on the Foundations of Software Engineering (ESEC/FSE'07). Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. Pradella, M., Morzenti, A., and San Pietro, P. 2008a. Benchmarking model- and satisfiability-checking on bi-infinite time. In Proceedings of the 5th International Colloquium on Theoretical Aspects of Computing (ICTAC'08). Lecture Notes in Computer Science, vol. 5160, Springer, 290--304. Google ScholarGoogle ScholarDigital LibraryDigital Library
  49. Pradella, M., Morzenti, A., and San Pietro, P. 2008b. Refining real-time system specifications through bounded model- and satisfiability-checking. In Proceedings of the 23rd IEEE/ACM International Conference on Automated Software Engineering (ASE'08). 119--127. Google ScholarGoogle ScholarDigital LibraryDigital Library
  50. Pradella, M., Morzenti, A., and San Pietro, P. 2009. A metric encoding for bounded model checking. In Proceedings of the 2nd World Congress on Formal Methods (FM'09). A. Cavalcanti and D. Dams, Eds., Lecture Notes in Computer Science, vol. 5850, Springer, 741--756. Google ScholarGoogle ScholarDigital LibraryDigital Library
  51. Pradella, M., San Pietro, P., Spoletini, P., and Morzenti, A. 2003. Practical model checking of ltl with past. In Proceedings of the International Symposium on Automated Technology for Verification and Analysis (ATVA'03).Google ScholarGoogle Scholar
  52. Prior, A. 1967. Past, Present and Future. Oxford University Press, Oxford, UK.Google ScholarGoogle Scholar
  53. Rescher, N. and Urquhart, A. 1971. Temporal Logic. Springer, New York.Google ScholarGoogle Scholar
  54. Rozier, K. Y. and Vardi, M. Y. 2007. LTL satisfiability checking. In Proceedings of the 14th International SPIN Conference on Model Checking Software. Lecture Notes in Computer Science, vol. 4595, Springer, 149--167. Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. San Pietro, P., Morzenti, A., and Morasca, S. 2000. Generation of execution sequences for modular time critical systems. IEEE Trans. Softw. Engin. 26, 2, 128--149. Google ScholarGoogle ScholarDigital LibraryDigital Library

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                      cover image ACM Transactions on Software Engineering and Methodology
                      ACM Transactions on Software Engineering and Methodology  Volume 22, Issue 3
                      In memoriam, fault detection and localization, formal methods, modeling and design
                      July 2013
                      414 pages
                      ISSN:1049-331X
                      EISSN:1557-7392
                      DOI:10.1145/2491509
                      Issue’s Table of Contents

                      Copyright © 2013 ACM

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                      Publication History

                      • Published: 30 July 2013
                      • Accepted: 1 March 2012
                      • Revised: 1 February 2012
                      • Received: 1 July 2010
                      Published in tosem Volume 22, Issue 3

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