Abstract
LTL ∖ GU is a fragment of linear temporal logic (LTL), where negations appear only on propositions, and formulas are built using the temporal operators X (next), F (eventually), G (always), and U (until, with the restriction that no until operator occurs in the scope of an always operator. Our main result is the construction of Limit Deterministic Büchi automata for this logic that are exponential in the size of the formula. One consequence of our construction is a new, improved EXPTIME model checking algorithm (as opposed to the previously known doubly exponential time) for Markov Decision Processes and LTL ∖ GU formulae. Another consequence is that it gives us a way to construct exponential sized Probabilistic Büchi Automata for LTL ∖ GU.
Chapter PDF
Similar content being viewed by others
References
Alur, R., Torre, S.L.: Deterministic generators and games for ltl fragments. ACM Trans. Comput. Logic 5(1), 1–25 (2004)
Babiak, T., Blahoudek, F., Křetínský, M., Strejček, J.: Effective translation of LTL to deterministic Rabin automata: Beyond the (F,G)-fragment. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 24–39. Springer, Heidelberg (2013)
Baier, C., Größer, M.: Recognizing omega-regular languages with probabilistic automata. In: LICS, pp. 137–146 (2005)
Chadha, R., Sistla, A.P., Viswanathan, M.: On the expressiveness and complexity of randomization in finite state monitors. J. ACM 56(5), 26:1–26:44 (2009)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42(4), 857–907 (1995)
Esparza, J., Křetínský, J.: From LTL to deterministic automata: A safraless compositional approach. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 192–208. Springer, Heidelberg (2014)
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)
Kini, D., Viswanathan, M.: Probabilistic automata for safety LTL specifications. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 118–136. Springer, Heidelberg (2014)
Kini, D., Viswanathan, M.: Probabilistic büchi automata for LTL∖GU. Technical Report University of Illinois at Urbana-Champaign (2015), http://hdl.handle.net/2142/72686
Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theoretical Computer Science 363(2), 182–195 (2006)
Křetínský, J., Esparza, J.: Deterministic automata for the (F,G)-fragment of LTL. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 7–22. Springer, Heidelberg (2012)
Křetínský, J., Garza, R.L.: Rabinizer 2: Small deterministic automata for LTL∖ GU. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 446–450. Springer, Heidelberg (2013)
Morgenstern, A., Schneider, K.: From LTL to symbolically represented deterministic automata. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 279–293. Springer, Heidelberg (2008)
Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2006)
Pnueli, A., Zaks, A.: On the merits of temporal testers. In: 25 Years of Model Checking, pp. 172–195 (2008)
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)
Vardi, M., Wolper, P., Sistla, A.P.: Reasoning about infinite computation paths. In: FOCS (1983)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kini, D., Viswanathan, M. (2015). Limit Deterministic and Probabilistic Automata for LTL ∖ GU. In: Baier, C., Tinelli, C. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2015. Lecture Notes in Computer Science(), vol 9035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46681-0_57
Download citation
DOI: https://doi.org/10.1007/978-3-662-46681-0_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-46680-3
Online ISBN: 978-3-662-46681-0
eBook Packages: Computer ScienceComputer Science (R0)