Abstract
There are two main classes of methods for checking universality and language inclusion of Büchi-automata: Rank-based methods and Ramsey-based methods. While rank-based methods have a better worst-case complexity, Ramsey-based methods have been shown to be quite competitive in practice [10,9]. It was shown in [10] (for universality checking) that a simple subsumption technique, which avoids exploration of certain cases, greatly improves the performance of the Ramsey-based method. Here, we present a much more general subsumption technique for the Ramsey-based method, which is based on using simulation preorder on the states of the Büchi-automata. This technique applies to both universality and inclusion checking, yielding a substantial performance gain over the previous simple subsumption approach of [10].
This work was supported in part by the Royal Society grant JP080268, the Czech Science Foundation (projects P103/10/0306 and 102/09/H042), the Czech Ministry of Education (projects COST OC10009 and MSM 0021630528), the internal BUT FIT grant FIT-10-1, the UPMARC project, the CONNECT project, National Science Council of Taiwan project no. 99-2218-E-001-002-MY3, and the ESF project Games for Design and Verification.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdulla, P.A., Chen, Y.-F., Clemente, L., Holík, L., Hong, C.-D., Mayr, R., Vojnar, T.: Simulation Subsumption in Ramsey-based Büchi Automata Universality and Inclusion Testing. Technical report FIT-TR-2010-02, FIT BUT (2010), http://www.fit.vutbr.cz/~holik/pub/FIT-TR-2010-002.pdf
Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When Simulation Meets Antichains (On Checking Language Inclusion of Nondeterministic Finite (Tree) Automata). In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010)
Abdulla, P.A., Chen, Y.-F., Holík, L., Vojnar, T.: Mediating for Reduction (On Minimizing Alternating Büchi Automata). In: Proc. of FSTTCS’09, Leibniz International Proceedings in Informatics, vol. 4 (2009)
Büchi, J.R.: On a Decision Method in Restricted Second Order Arithmetic. In: Proc. of Int. Con. on Logic, Method, and Phil. of Science (1962)
Doyen, L., Raskin, J.-F.: Improved Algorithms for the Automata-based Approach to Model Checking. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 451–465. Springer, Heidelberg (2007)
Etessami, K.: A Hierarchy of Polynomial-Time Computable Simulations for Automata. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, p. 131. Springer, Heidelberg (2002)
Etessami, K., Wilke, T., Schuller, R.A.: Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata. SIAM J. Comp. 34(5) (2005)
Fogarty, S.: Büchi Containment and Size-Change Termination. Master’s Thesis, Rice University (2008)
Fogarty, S., Vardi, M.Y.: Büchi Complementation and Size-Change Termination. In: Proc. of TACAS’09. LNCS, vol. 5505. Springer, Heidelberg (2009)
Fogarty, S., Vardi, M.Y.: Efficient Büchi Universality Checking. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 205–220. Springer, Heidelberg (2010)
Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing Simulations on Finite and Infinite Graphs. In: Proc. FOCS’95. IEEE CS, Los Alamitos (1995)
Holík, L., Šimáček, J.: Optimizing an LTS-Simulation Algorithm. In: Proc. of MEMICS’09 (2009)
Jones, N.D., Lee, C.S., Ben-Amram, A.M.: The Size-Change Principle for Program Termination. In: Proc. of POPL’01. ACM SIGPLAN (2001)
Kupferman, O., Vardi, M.Y.: Weak Alternating Automata Are Not That Weak. ACM Transactions on Computational Logic 2(2), 408–429 (2001)
Pelánek, R.: BEEM: Benchmarks for Explicit Model Checkers. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 263–267. Springer, Heidelberg (2007)
Sistla, A.P., Vardi, M.Y., Wolper, P.: The Complementation Problem for Büchi Automata with Applications to Temporal Logic. In: Brauer, W. (ed.) ICALP 1985. LNCS, vol. 194. Springer, Heidelberg (1985)
Somenzi, F., Bloem, R.: Efficient Büchi Automata from LTL Formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855. Springer, Heidelberg (2000)
Tabakov, D., Vardi, M.Y.: Model Checking Büchi Specifications. In: Proc. of LATA’07 (2007)
Tsay, Y.-K., Chen, Y.-F., Tsai, M.-H., Wu, K.-N., Chan, W.-C.: GOAL: A Graphical Tool for Manipulating Büchi Automata and Temporal Formulae. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 466–471. Springer, Heidelberg (2007)
Wulf, M.D., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: A New Algorithm for Checking Universality of Finite Automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)
http://iis.sinica.edu.tw/FMLAB/CAV2010 (capitalize “FMLAB” and “CAV 2010”)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abdulla, P.A. et al. (2010). Simulation Subsumption in Ramsey-Based Büchi Automata Universality and Inclusion Testing. In: Touili, T., Cook, B., Jackson, P. (eds) Computer Aided Verification. CAV 2010. Lecture Notes in Computer Science, vol 6174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14295-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-14295-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14294-9
Online ISBN: 978-3-642-14295-6
eBook Packages: Computer ScienceComputer Science (R0)