Abstract
We develop a generic technique to compute minimal separating DFAs (deterministic finite automata) and regular invariants. Our technique works by expressing the desired properties of a solution in terms of logical formulae and using SAT or SMT solvers to find solutions. We apply our technique to three concrete problems: computing minimal separating DFAs (e.g., used in compositional verification), regular model checking, and synthesizing loop invariants of integer programs that are expressible in Presburger arithmetic.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bardin, S., Leroux, J., Point, G.: FAST Extended Release. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 63–66. Springer, Heidelberg (2006)
Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58, 117–148 (2003)
Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Transactions on Computers C-21(6), 592–597 (1972)
Bouajjani, A., Jonsson, B., Nilsson, M., Touili, T.: Regular Model Checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 403–418. Springer, Heidelberg (2000)
Chen, Y.-F., Farzan, A., Clarke, E.M., Tsay, Y.-K., Wang, B.-Y.: Learning Minimal Separating DFA’s for Compositional Verification. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 31–45. Springer, Heidelberg (2009)
Gupta, A., Rybalchenko, A.: InvGen: An Efficient Invariant Generator. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 634–640. Springer, Heidelberg (2009)
Henriksen, J.G., Jensen, J.L., Jørgensen, M.E., Klarlund, N., Paige, R., Rauhe, T., Sandholm, A.: Mona: Monadic Second-order Logic in Practice. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 89–110. Springer, Heidelberg (1995)
Jhala, R., McMillan, K.L.: A Practical and Complete Approach to Predicate Refinement. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 459–473. Springer, Heidelberg (2006)
Legay, A.: Generic Techniques for the Verification of Infinite-State Systems. Ph.D. thesis, Universite de Liege (2007)
Legay, A.: T(O)RMC: A Tool for (ω)-Regular Model Checking. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 548–551. Springer, Heidelberg (2008)
Leroux, J.: A polynomial time presburger criterion and synthesis for number decision diagrams. In: LICS, pp. 147–156. IEEE Computer Society (2005)
Neider, D.: Reachability Games on Automatic Graphs. In: Domaratzki, M., Salomaa, K. (eds.) CIAA 2010. LNCS, vol. 6482, pp. 222–230. Springer, Heidelberg (2011)
Pena, J.M., Oliveira, A.L.: A new algorithm for the reduction of incompletely specified finite state machines. In: ICCAD, pp. 482–489 (1998)
Pfleeger, C.: State reduction in incompletely specified finite-state machines. IEEE Transactions on Computers C-22(12), 1099–1102 (1973)
Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Scalable Analysis of Linear Systems Using Mathematical Programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 25–41. Springer, Heidelberg (2005)
Vardhan, A., Viswanathan, M.: LEVER: A Tool for Learning Based Verification. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 471–474. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Neider, D. (2012). Computing Minimal Separating DFAs and Regular Invariants Using SAT and SMT Solvers. In: Chakraborty, S., Mukund, M. (eds) Automated Technology for Verification and Analysis. ATVA 2012. Lecture Notes in Computer Science, vol 7561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33386-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-33386-6_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33385-9
Online ISBN: 978-3-642-33386-6
eBook Packages: Computer ScienceComputer Science (R0)