Abstract
Temporal logics like LTL are frequently used for the specification and verification of reactive systems. For verification, LTL formulas are typically translated to generalized nondeterministic Büchi automata so that the verification problem is reduced to checking the emptiness of automata. While this can be done symbolically for nondeterministic automata, other applications require deterministic automata, so that a subsequent determinization step is required. Unfortunately, currently known determinization procedures for Büchi automata like Safra’s procedure are not amenable to a symbolic implementation.
It is well-known that ω-automata that stem from LTL formulas have special properties. In this paper, we exploit such a property in a new determinization procedure for these automata. Our procedure avoids the use of complicated tree structures as used in Safra’s procedure and it generates symbolic descriptions of equivalent deterministic parity automata which was so far not possible for full LTL.
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Allauzen, C., Mohri, M.: An efficient pre-determinization algorithm. In: H. Ibarra, O., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 83–95. Springer, Heidelberg (2003)
Armoni, R., et al.: Efficient LTL compilation for SAT-based model checking. In: Conference on Computer Aided Design (ICCAD), pp. 877–884. IEEE Computer Society, Los Alamitos (2005)
Bloem, R., et al.: Symbolic implementation of alternating automata. In: H. Ibarra, O., Yen, H.-C. (eds.) CIAA 2006. LNCS, vol. 4094, pp. 208–218. Springer, Heidelberg (2006)
Burch, J., et al.: Symbolic model checking: 1020 states and beyond. In: Logic in Computer Science (LICS), Washington, DC, USA, 1990, pp. 1–33. IEEE Computer Society, Los Alamitos (1990)
Carton, O., Michel, M.: Unambiguous Büchi automata. Theoretical Computer Science 297(1-3), 37–81 (2003)
Clarke, E., Grumberg, O., Hamaguchi, K.: Another look at LTL model checking. Formal Methods in System Design (FMSD) 10(1), 47–71 (1997)
Emerson, E.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, ch.16, vol. B, pp. 995–1072. Elsevier, Amsterdam (1990)
Emerson, E., Sistla, A.: Deciding branching time logic. In: Symposium on Theory of Computing (STOC), pp. 14–24 (1984)
Gastin, P., Oddoux, D.: Fast LTL to Büchi Automata Translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, Springer, Heidelberg (2001)
Gurumurthy, S., et al.: On Complementing Nondeterministic Büchi Automata. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 96–110. Springer, Heidelberg (2003)
Henzinger, T., Piterman, N.: Solving games without determinization. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 394–409. Springer, Heidelberg (2006)
Kesten, Y., Pnueli, A., Raviv, L.: Algorithmic Verification of Linear Temporal Logic Specifications. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, Springer, Heidelberg (1998)
Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of temporal logic. Theoretical Computer Science 363(2), 182–195 (2006)
Kupferman, O., Piterman, N., Vardi, M.: Safraless Compositional Synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006)
Kupferman, O., Vardi, M.: Safraless decision procedures. In: Symposium on Foundations of Computer Science, pp. 531–540. IEEE Computer Society, Los Alamitos (2005)
McNaughton, R., Papert, S.: Counter-free Automata. MIT Press, Cambridge (1971)
Merz, S., Sezgin, A.: Emptiness of linear weak alternating automata. Technical report, LORIA (2003)
Muller, D., Saoudi, A., Schupp, P.: Alternating automata, the weak monadic theory of the tree, and its complexity. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 275–283. Springer, Heidelberg (1986)
Pelánek, R., Strejcek, J.: Deeper connections between LTL and alternating automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 238–249. Springer, Heidelberg (2006)
Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. In: Symp. on Logic in Computer Science, IEEE Comp. Soc, Los Alamitos (2006)
Pnueli, A.: The temporal logic of programs. In: Foundations of Computer Science (FOCS), Providence, RI, USA, 1977, pp. 46–57. IEEE Computer Society, Los Alamitos (1977)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Symposium on Principles of Programming Languages, Austin, Texas, pp. 179–190. ACM, New York (1989)
Safra, S.: On the complexity of ω-automata. In: Symposium on Foundations of Computer Science (FOCS), pp. 319–327 (1988)
Schneider, K.: Improving automata generation for linear temporal logic by considering the automata hierarchy. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 39–54. Springer, Heidelberg (2001)
Schneider, K.: Verification of Reactive Systems – Formal Methods and Algorithms. In: Texts in Theoretical Computer Science. EATCS Series, Springer, Heidelberg (2003)
Schulte Althoff, C., Thomas, W., Wallmeier, N.: Observations on determinization of Büchi automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 262–272. Springer, Heidelberg (2006)
Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, ch. 4, vol. B, pp. 133–191. Elsevier, Amsterdam (1990)
Tuerk, T., Schneider, K.: Relationship between alternating omega-automata and symbolically represented nondeterministic omega-automata. Technical Report 340, Dep. of Computer Science, University of Kaiserslautern, Germany (2005)
Vardi, M.: 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)
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)
Vardi, M., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Symposium on Logic in Computer Science (LICS), pp. 332–344. IEEE Computer Society, Los Alamitos (1986)
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Morgenstern, A., Schneider, K. (2008). From LTL to Symbolically Represented Deterministic Automata. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2008. Lecture Notes in Computer Science, vol 4905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78163-9_24
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DOI: https://doi.org/10.1007/978-3-540-78163-9_24
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