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\(2^5\) Years of Model Checking

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Perspectives of System Informatics (PSI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8974))

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Abstract

Model Checking is an automatic verification technique for large state transition systems. It was originally developed for reasoning about finite-state concurrent systems. The technique has been used successfully to debug complex computer hardware, communication protocols, and software. It is beginning to be used for analyzing cyber-physical, biological, and financial systems as well. The major challenge for the technique is a phenomenon called the State Explosion Problem. This issue is impossible to avoid in the worst case; but, by using sophisticated data structures and clever search algorithms, it is now possible to verify state transition systems with an astronomical number of states. In this paper, we will briefly review the development of Model Checking over the past 32 years, with an emphasis on model checking stochastic hybrid systems.

This paper has been partly supported by the Office of Naval Research (ONR) under grant 29749-1-1141240.

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References

  1. Abate, A.: Probabilistic reachability for stochastic hybrid systems: theory, computations, and applications. ProQuest (2007)

    Google Scholar 

  2. Abate, A., Katoen, J.-P., Lygeros, J., Prandini, M.: A two-step scheme for approximate model checking of stochastic hybrid systems. In: Proceedings of the 18th IFAC World Congress, IFAC (2011)

    Google Scholar 

  3. Abate, A., Katoen, J.-P., Mereacre, A.: Quantitative automata model checking of autonomous stochastic hybrid systems. In: Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control, pp. 83–92. ACM (2011)

    Google Scholar 

  4. Amin, S., Abate, A., Prandini, M., Lygeros, J., Sastry, S.S.: Reachability analysis for controlled discrete time stochastic hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 49–63. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley - Interscience, New York (1974)

    MATH  Google Scholar 

  6. Ball, T., Rajamani, S.K.: The SLAM toolkit. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 260–264. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Bellman, R.: A Markovian decision process. Technical report, DTIC Document (1957)

    Google Scholar 

  9. Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Bloem, R., Ravi, K., Somenzi, F.: Efficient decision procedures for model checking of linear time logic properties. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 222–235. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Blom, H.A., Bloem, E.A.: Particle filtering for stochastic hybrid systems. In: 43rd IEEE Conference on Decision and Control, vol. 3, pp. 3221–3226. IEEE (2004)

    Google Scholar 

  12. Blom, H.A., Lygeros, J., Everdij, M., Loizou, S., Kyriakopoulos, K.: Stochastic Hybrid Systems: Theory and Safety Critical Applications. Springer, Heidelberg (2006)

    Book  Google Scholar 

  13. Brayton, R.K., et al.: VIS: a system for verification and synthesis. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 428–432. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  14. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 100(8), 677–691 (1986)

    Article  Google Scholar 

  15. Bujorianu, M.L., Lygeros, J.: General stochastic hybrid systems. In: IEEE Mediterranean Conference on Control and Automation MED, vol. 4, pp. 174–188 (2004)

    Google Scholar 

  16. Burch, J., Clarke, E.M., Long, D.: Symbolic model checking with partitioned transition relations. In: Computer Science Department, p. 435 (1991)

    Google Scholar 

  17. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L.: Sequential circuit verification using symbolic model checking. In: 27th ACM/IEEE Design Automation Conference, pp. 46–51. IEEE (1990)

    Google Scholar 

  18. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.-J.: Symbolic model checking: \(10^{20}\) states and beyond. In: Fifth Annual IEEE Symposium on Logic in Computer Science, pp. 428–439. IEEE (1990)

    Google Scholar 

  19. Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: NuSMV: a new symbolic model checker. Int. J. Softw. Tools Technol. Transf. 2(4), 410–425 (2000)

    Article  MATH  Google Scholar 

  20. Claessen, K., Fisher, J., Ishtiaq, S., Piterman, N., Wang, Q.: Model-checking signal transduction networks through decreasing reachability sets. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 85–100. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  22. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  23. Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Program. Lang. Syst. (TOPLAS) 16(5), 1512–1542 (1994)

    Article  Google Scholar 

  24. Cordeiro, L., Fischer, B., Marques-Silva, J.: SMT-based bounded model checking for embedded ANSI-C software. IEEE Trans. Softw. Eng. 38(4), 957–974 (2012)

    Article  Google Scholar 

  25. D’Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G.: Reachability analysis of probabilistic systems by successive refinements. In: de Luca, L., Gilmore, S. (eds.) PAPM-PROBMIV 2001. LNCS, vol. 2165, pp. 39–56. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Davis, M.H.: Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. Royal Stat.Soc. Ser. B (Methodol.) 46(3), 353–388 (1984)

    MATH  Google Scholar 

  27. de Moura, L., Bjørner, 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 

  28. Dutertre, B., De Moura, L.: The yices SMT solver. 2, 2 (2006). Tool paper at http://yices.csl.sri.com/tool-paper.pdf

  29. Fränzle, M., Hahn, E.M., Hermanns, H., Wolovick, N., Zhang, L.: Measurability and safety verification for stochastic hybrid systems. In: Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control, pp. 43–52. ACM (2011)

    Google Scholar 

  30. Fränzle, M., Hermanns, H., Teige, T.: Stochastic satisfiability modulo theory: a novel technique for the analysis of probabilistic hybrid systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 172–186. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  31. Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  32. Ganai, M.K., Gupta, A., Ashar, P.: Efficient SAT-based unbounded symbolic model checking using circuit co-factoring. In: Proceedings of the 2004 IEEE/ACM International Conference on Computer-Aided Design, pp. 510–517. IEEE (2004)

    Google Scholar 

  33. Godefroid, P.: Using partial orders to improve automatic verification methods. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 176–185. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  34. Hahn, E.M., Norman, G., Parker, D., Wachter, B., Zhang, L.: Game-based abstraction and controller synthesis for probabilistic hybrid systems. In: 2011 Eighth International Conference on Quantitative Evaluation of Systems (QEST), pp. 69–78. IEEE (2011)

    Google Scholar 

  35. Hardin, R., Kurshan, R., Shukla, S., Vardi, M.: A new heuristic for bad cycle detection using BDDs. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 268–278. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  36. Havelund, K., Shankar, N.: Experiments in theorem proving and model checking for protocol verification. In: Gaudel, M.-C., Wing, J.M. (eds.) FME 1996. LNCS, vol. 1051, pp. 662–681. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  37. Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Software verification with BLAST. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 235–239. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  38. Hermanns, H., Wachter, B., Zhang, L.: Probabilistic CEGAR. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 162–175. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  39. Holzmann, G.J.: The model checker SPIN. IEEE Trans. Softw. Eng. 23(5), 279–295 (1997)

    Article  MathSciNet  Google Scholar 

  40. Hu, J., Lygeros, J., Sastry, S.: Towards a theory of stochastic hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 160–173. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  41. Katoen, J.-P., Khattri, M., Zapreev, I.S.: A Markov reward model checker. In: Second International Conference on the Quantitative Evaluation of Systems, pp. 243–244. IEEE (2005)

    Google Scholar 

  42. Kroening, D., Tautschnig, M.: CBMC – C bounded model checker. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 389–391. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  43. Kwiatkowska, M., Norman, G., Parker, D.: Game-based abstraction for Markov decision processes. In: Third International Conference on Quantitative Evaluation of Systems, pp. 157–166. IEEE (2006)

    Google Scholar 

  44. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  45. Marrero, W., Clarke, E., Jha, S.: Model checking for security protocols. Technical report, DTIC Document (1997)

    Google Scholar 

  46. McMillan, K.L.: Symbolic Model Checking. Springer, New York (1993)

    Book  MATH  Google Scholar 

  47. McMillan, K.L.: Applying SAT methods in unbounded symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 250–264. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  48. McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  49. Peled, D.: All from one, one for all: on model checking using representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  50. Platzer, A.: Stochastic differential dynamic logic for stochastic hybrid programs. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 446–460. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  51. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE (1977)

    Google Scholar 

  52. Queille, J.-P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  53. Riley, D., Koutsoukos, X.D., Riley, K.: Modeling and simulation of biochemical processes using stochastic hybrid systems: the sugar cataract development process. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 429–442. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  54. Sebastiani, R., Tonetta, S., Vardi, M.Y.: Symbolic systems, explicit properties: on hybrid approaches for LTL symbolic model checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 350–363. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  55. Sheeran, M., Singh, S., Stålmarck, G.: Checking safety properties using induction and a SAT-solver. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 108–125. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  56. Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 31–45. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  57. Sproston, J.: Model checking for probabilistic timed and hybrid systems. Ph.D. thesis. School of Computer Science, University of Birmingham (2001)

    Google Scholar 

  58. Tijms, H.C.: A First Course in Stochastic Models. Wiley, New York (2003)

    Book  MATH  Google Scholar 

  59. Tinelli, C.: SMT-based model checking. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, p. 1. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  60. Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  61. Wachter, B., Zhang, L.: Best probabilistic transformers. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 362–379. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  62. Wang, Q., Zuliani, P., Kong, S., Gao, S., Clarke, E.M.: SReach: a bounded model checker for stochastic hybrid systems. CoRR, abs/1404.7206 (2014)

    Google Scholar 

  63. Wang, Q., Zuliani, P., Kong, S., Gao, S., Clarke, E.M.: SReach: combining statistical tests and bounded model checking for nonlinear hybrid systems with parametric uncertainty. Technical report, Computer Science Department, Carnegie Mellon University (2014)

    Google Scholar 

  64. Wimmer, R., Braitling, B., Becker, B.: Counterexample generation for discrete-time markov chains using bounded model checking. In: Jones, N.D., Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 366–380. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  65. Younes, H.L.S.: Ymer: a statistical model checker. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 429–433. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  66. Zhang, L., She, Z., Ratschan, S., Hermanns, H., Hahn, E.M.: Safety verification for probabilistic hybrid systems. Eur. J. Control 18(6), 572–587 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  67. Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to simulink/stateflow verification. In: Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, pp. 243–252. ACM (2010)

    Google Scholar 

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  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, USA

    Edmund M. Clarke & Qinsi Wang

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  1. Edmund M. Clarke
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Correspondence to Edmund M. Clarke .

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  1. School of Computer Science, University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

  2. A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia

    Irina Virbitskaite

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Clarke, E.M., Wang, Q. (2015). \(2^5\) Years of Model Checking. In: Voronkov, A., Virbitskaite, I. (eds) Perspectives of System Informatics. PSI 2014. Lecture Notes in Computer Science(), vol 8974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46823-4_2

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