Abstract
We propose to use the knowledge that an ω-regular property is stutter insensitive to construct potentially smaller deterministic ω-automata for such a property, e.g. using Safra’s determinization construction. This knowledge allows us to skip states that are redundant under stuttering, which can reduce the size of the generated automaton. In order to use this technique even for automata that are not completely insensitive to stuttering, we introduce the notion of partial stutter insensitiveness and apply our construction only on the subset of symbols for which stuttering is allowed. We evaluate the benefits of this heuristic in practice using multiple sets of benchmark formulas.
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References
Thomas, W.: Languages, automata, and logic. Handbook of formal languages 3, 389–455 (1997)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS, pp. 332–344. IEEE Computer Society Press, Los Alamitos (1986)
Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)
Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57. IEEE Computer Society Press, Los Alamitos (1977)
de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, Department of Computer Science (1997)
Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11, 125–155 (1998)
Vardi, M.: Probabilistic linear-time model checking: An overview of the automata-theoretic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999)
Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theoretical Computer Science 363, 182–195 (2006)
Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, The Weizmann Institute of Science, Rehovot, Israel (1989)
Ciesinski, F., Baier, C.: LiQuor: A tool for qualitative and quantitative linear time analysis of reactive systems. In: QEST, pp. 131–132. IEEE Computer Society Press, Los Alamitos (2006)
Lamport, L.: What Good is Temporal Logic? In: IFIP Congress, pp. 657–668 (1983)
Holzmann, G.J., Peled, D.: An improvement in formal verification. In: FORTE, pp. 197–211. Chapman & Hall, Sydney, Australia (1994)
Valmari, A.: A stubborn attack on state explosion. Formal Methods in System Design 1, 297–322 (1992)
Baier, C., D’Argenio, P.R., Größer, M.: Partial order reduction for probabilistic branching time. Electr. Notes Theor. Comput. Sci. 153, 97–116 (2006)
Etessami, K.: Stutter-invariant languages, omega-automata, and temporal logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 236–248. Springer, Heidelberg (1999)
Peled, D., Wilke, T.: Stutter-invariant temporal properties are expressible without the next-time operator. Inf. Process. Lett. 63, 243–246 (1997)
Peled, D., Wilke, T., Wolper, P.: An Algorithmic Approach for Checking Closure Properties of Temporal Logic Specifications and omega-Regular Languages. Theor. Comput. Sci. 195, 183–203 (1998)
Holzmann, G., Kupferman, O.: Not checking for closure under stuttering. In: Proceedings of the 2nd International Workshop on the SPIN Verification System, DIMCAS, pp. 163–169 (1996)
Etessami, K.: A note on a question of Peled and Wilke regarding stutter-invariant LTL. Inf. Process. Lett. 75, 261–263 (2000)
Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)
Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)
Somenzi, F., Bloem, R.: Efficient Büchi automata from LTL formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)
Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Patterns in property specifications for finite-state verification. In: ICSE, pp. 411–420 (1999)
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Klein, J., Baier, C. (2007). On-the-Fly Stuttering in the Construction of Deterministic ω-Automata. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_7
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DOI: https://doi.org/10.1007/978-3-540-76336-9_7
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