Abstract
Emptiness check is a key operation in the automata-theoretic approach to LTL verification. However, it is usually done on Büchi automata with a single acceptance condition. We review existing on-the-fly emptiness-check algorithms for generalized Büchi automata (i.e., with multiple acceptance conditions) and show how they compete favorably with emptiness-checks for degeneralized automata, especially in presence of weak fairness assumptions. We also introduce a new emptiness-check algorithm, some heuristics to improve existing checks, and propose algorithms to compute accepting runs in the case of multiple acceptance conditions.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Černá, I., Pelánek, R.: Relating hierarchy of temporal properties to model checking. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 318–327. Springer, Heidelberg (2003)
Courcoubetis, C., Vardi, M.Y., Wolper, P., Yannakakis, M.: Memory-efficient algorithm for the verification of temporal properties. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 233–242. Springer, Heidelberg (1991)
Couvreur, J.-M.: On-the-fly verification of temporal logic. In: Wing, J.M., Woodcock, J.C.P., Davies, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253–271. Springer, Heidelberg (1999)
Duret-Lutz, A., Poitrenaud, D.: Spot: an extensible model checking library using transition-based generalized Büchi automata. In: Proc. of MASCOTS 2004, pp. 76–83. IEEE Computer Society, Los Alamitos (2004)
Dwyer, M.B., Avrunin, G.S., Corbett, J.C.: Property specification patterns for finite-state verification. In: Proc. of FMSP 1998, pp. 7–15. ACM, New York (1998)
Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)
Gastin, P., Moro, P., Zeitoun, M.: Minimization of counterexamples in SPIN. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 92–108. Springer, Heidelberg (2004)
Geldenhuys, J., Valmari, A.: Tarjan’s algorithm makes on-the-fly LTL verification more efficient. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 205–219. Springer, Heidelberg (2004)
Geldenhuys, J., Valmari, A.: More efficient on-the-fly LTL verification with Tarjan’s algorithm. Theoretical Computer Science (2005); To appear: conference paper selected for journal publication
Giannakopoulou, D., Lerda, F.: From states to transitions: Improving translation of LTL formulæ to Büchi automata. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 308–326. Springer, Heidelberg (2002)
Godefroid, P., Holzmann, G.J.: On the verification of temporal properties. In: Proc. of PSTV 1993. IFIP Transactions, vol. C-16, pp. 109–124. North-Holland, Amsterdam (1993)
Hammer, M., Knapp, A., Merz, S.: Truly on-the-fly LTL model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 191–205. Springer, Heidelberg (2005)
Holzmann, G.J.: The Spin Model Checker: Primer and Reference Manual. Addison-Wesley, Reading (2003) ISBN 0-321-22862-6
Holzmann, G.J., Peled, D.A., Yannakakis, M.: On nested depth first search. In: Proc. of SPIN 1996, May 1996. DIMACS, AMS vol. 32 (1996)
Latvala, T., Heljanko, K.: Coping with strong fairness. Fundamenta Informaticae 43(1-4), 1–19 (2000)
Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: Proc. of POPL 1985, pp. 97–107. ACM, New York (1985)
Schwoon, S., Esparza, J.: A note on on-the-fly verification algorithms. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 174–190. Springer, Heidelberg (2005)
Somenzi, F., Bloem, R.: Efficient Büchi automata for LTL formulæ. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 247–263. Springer, Heidelberg (2000)
Tauriainen, H.: On translating linear temporal logic into alternating and nondeterministic automata. Research Report A83, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland (December 2003)
Tauriainen, H.: Nested emptiness search for generalized Büchi automata. In: Proc. of ACSD 2004, pp. 165–174. IEEE Computer Society, Los Alamitos (2004)
Tauriainen, H.: A randomized testbench for algorithms translating linear temporal logic formulæ into Büchi automata. In: Proc. of CS&P 1999, September 1999, pp. 251–262 (1999)
Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Proc. of Banff 1994. LNCS, vol. 1043. Springer, Heidelberg (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Couvreur, JM., Duret-Lutz, A., Poitrenaud, D. (2005). On-the-Fly Emptiness Checks for Generalized Büchi Automata. In: Godefroid, P. (eds) Model Checking Software. SPIN 2005. Lecture Notes in Computer Science, vol 3639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537328_15
Download citation
DOI: https://doi.org/10.1007/11537328_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28195-5
Online ISBN: 978-3-540-31899-6
eBook Packages: Computer ScienceComputer Science (R0)