Abstract
Verification by network invariants is a heuristic to solve uniform verification of parameterized systems. Given a system P, a network invariant for P is a system that abstracts the composition of every number of copies of P running in parallel. If there is such a network invariant, by reasoning about it, uniform verification with respect to the family P[1] ∥ ⋯ ∥ P[n] can be carried out. In this paper, we propose a procedure that searches systematically for a network invariant satisfying a given safety property. The search is based on algorithms for learning finite automata due to Angluin and Biermann. We optimize the search by combining both algorithms for improving successive possible invariants. We also show how to reduce the learning problem to SAT, allowing efficient SAT solvers to be used, which turns out to yield a very competitive learning algorithm. The overall search procedure finds a minimal such invariant, if it exists.
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Keywords
- Constraint Satisfaction Problem
- Regular Language
- Conjunctive Normal Form
- Safety Property
- Network Invariant
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Krzysztof, R.: Apt and Dexter Kozen. Limits for automatic verification of finite-state concurrent systems. IPL 22(6), 307–309 (1986)
Alur, R., Madhusudan, P., Nam, W.: Symbolic compositional verification by learning assumptions. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 548–562. Springer, Heidelberg (2005)
Angluin, D.: Learning regaular sets from queries and counterexamples. IC 75, 87–106 (1987)
Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behaviour. IEEE TOC 21, 592–597 (1972)
Berg, T., Jonsson, B., Leucker, M., Saksena, M.: Insights to Angluin’s learning. TR 2003-039, Uppsala University (2003)
Chaki, S., Clarke, E.M., Sinha, N., Thati, P.: Automated assume-guarrantee reasoning for simulation conformance. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 534–547. Springer, Heidelberg (2005)
Clarke, E.M., 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)
Clarke, E.M., Talupur, M., Veith, H.: Environment abstraction for parameterized verification. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 126–141. Springer, Heidelberg (2005)
Emerson, E.A., Kahlon, V.: Reducing model checking of the many to the few. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 236–254. Springer, Heidelberg (2000)
Emerson, E.A., Namjoshi, K.S.: Reasoning about rings. In: POPL (1995)
Gold, E.M.: Complexity of automaton identification from given data. IC 37(3), 302–320 (1978)
Habermehl, P., Vojnar, T.: Regular model checking using inference of regular languages. ENTCS 138(3), 21–36 (2005)
Jonsson, B., Nilsson, M.: Transitive closures of regular relations for verifying infinite-state systems. In: Schwartzbach, M.I., Graf, S. (eds.) ETAPS 2000 and TACAS 2000. LNCS, vol. 1785, Springer, Heidelberg (2000)
Kurshan, R.P., McMillan, K.L.: A structural induction theorem for processes. IC 117(1), 1–11 (1995)
Kesten, Y., Pnueli, A.: Control and data abstraction: The cornerstones of practical formal verification. STTT 2(4), 328–342 (2000)
Kesten, Y., Piterman, N., Pnueli, A.: Bridging the gap between fair simulation and trace inclusion. IC 200(1), 35–61 (2005)
Kesten, Y., Pnueli, A., Shahar, E., Zuck, L.: Network invariants in action. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, p. 2002. Springer, Heidelberg (2002)
Lang, K.J.: Random dfa’s can be approximately learned from sparse uniform examples. In: COLT, pp. 45–52 (1992)
Lesens, D., Halbwachs, N., Raymond, P.: Automatic verification of parameterized linear networks of processes. In: 24th POPL (1997)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: DAC, pp. 530–535. ACM Press, New York (2001)
Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Pattern Recognition and Image Analysis. Series in Machine Perception and AI, vol. 1, pp. 49–61. World Scientific, Singapore (1992)
Oliveira, A.L., Silva, J.P.M.: Efficient algorithms for the inference of minimum size dfas. Machine Learning 44(1/2), 93–119 (2001)
Pena, J.M., Oliveira, A.L.: A new algorithm for the reduction of incompletely specified finite state machines. In: ICCAD, pp. 482–489 (1998)
Pnueli, A., Shahar, E.: A platform for combining deductive with algorithmic verification. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 184–195. Springer, Heidelberg (1996)
Pnueli, A., Shahar, E.: Liveness and acceleration in parameterized verification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 328–343. Springer, Heidelberg (2000)
Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Actively learning to verify safety for fifo automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 494–505. Springer, Heidelberg (2004)
Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Learning to verify safety properties. In: Davies, J., Schulte, W., Barnett, M. (eds.) ICFEM 2004. LNCS, vol. 3308, pp. 274–289. Springer, Heidelberg (2004)
Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Using language inference to verify omega-regular properties. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, Springer, Heidelberg (2005)
Wolper, P., Lovinfosse, V.: Verifying properties of large sets of processes with network invariants. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, Springer, Heidelberg (1990)
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Grinchtein, O., Leucker, M., Piterman, N. (2006). Inferring Network Invariants Automatically. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_40
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DOI: https://doi.org/10.1007/11814771_40
Publisher Name: Springer, Berlin, Heidelberg
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