Journal of Applied Mathematics

Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation

Laixiang Shan, Jun Qin, Mingshi Chen, and Zheng Qin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We present on-the-fly degeneralization algorithm used to transform generalized Büchi automata (GBA) into Büchi Automata (BA) different from the standard degeneralization algorithm. Contented situation, which is used to record what acceptance conditions are satisfiable during expanding LTL formulae, is attached to the states and transitions in the BA. In order to get the deterministic BA, the Shannon expansion is used recursively when we expand LTL formulae by applying the tableau rules. On-the-fly degeneralization algorithm is carried out in each step of the expansion of LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae. The temporary automata are stored as syntax directed acyclic graph in order to save storage space. These ideas are implemented in a conversion algorithm used to build a property automaton corresponding to the given LTL formulae. We compare our method to previous work and show that it is more efficient for four sets of random formulae generated by LBTT.

Article information

J. Appl. Math., Volume 2015 (2015), Article ID 516104, 10 pages.

First available in Project Euclid: 15 April 2015

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier


Shan, Laixiang; Qin, Jun; Chen, Mingshi; Qin, Zheng. Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation. J. Appl. Math. 2015 (2015), Article ID 516104, 10 pages. doi:10.1155/2015/516104.

Export citation


  • E. M. Clarke, O. Grumberg, and D. A. Peled, Model Checking, MIT Press, 1999.
  • T. Babiak, M. Ketnsk, V. ehk et al., “LTL to Büchi automata translation: fast and more deterministic,” in Tools and Algorithms for the Construction and Analysis of Systems, vol. 7214, pp. 95–109, Springer, Berlin, Germany, 2012.
  • P. Gastin and D. Oddoux, “Fast LTL to Büchi automata translation,” in Computer Aided Verification, G. Berry, H. Comon, and A. Finkel, Eds., vol. 2102 of Lecture Notes in Computer Science, pp. 53–65, Springer, 2001.
  • U. Boker, O. Kupferman, and A. Rosenberg, “Alternation removal in buchi automata,” in Automata, Languages and Programming, pp. 76–87, Springer, 2010.
  • A. Duret-Lutz, “Ltl translation improvements in spot,” in Proceedings of the 5th International Conference on Verification and Evaluation of Computer and Communication Systems (VECoS '11), pp. 72–83, British Computer Society, 2011.
  • J. M. Couvreur, “On-the-fly verification of linear temporal logic,” in FM99, Formal Methods, vol. 1708 of Lecture Notes in Computer Science, pp. 253–271, Springer, Berlin, Germany, 1999.
  • R. Gerth, D. Peled, M. Y. Vardi, and P. Wolper, “Simple on-the-fly automatic verification of linear temporal logic,” in Proceedings of the 15th IFIP WG6 International Symposium on Protocol Specification, Testing and Verification (IFIP '95), 1995.
  • G. J. Holzmann, “The model checker SPIN,” IEEE Transactions on Software Engineering, vol. 23, no. 5, pp. 279–295, 1997.
  • D. Giannakopoulou and F. Lerda, “From states to transitions: improving translation of LTL formulae to Büchi automata,” in Formal Techniques for Networked and Distributed Sytems–-FORTE 2002, vol. 2529 of Lecture Notes in Computer Science, pp. 308–326, Springer, Berlin, Germany, 2002.
  • T. Babiak, T. Badie, A. Duret-Lutz et al., “Compositional approach to suspension and other improvements to LTL translation,” in Model Checking Software, pp. 81–98, Springer, Berlin, Germany, 2013.
  • K. Chatterjee, A. Gaiser, and J. Ketnsk, “Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis,” in Computer Aided Verification, pp. 559–575, Springer, Berlin, Germany, 2013.
  • E. Renault, A. Duret-Lutz, F. Kordon, and D. Poitrenaud, “Three SCC-based emptiness checks for generalized Büchi automata,” in Logic for Programming, Artificial Intelligence, and Reasoning, vol. 8312 of Lecture Notes in Computer Science, pp. 668–682, Springer, Berlin, Germany, 2013.
  • A. Duret-Lutz and D. Poitrenaud, “SPOT: an extensible model checking library using transition-based generalized Büchi automata,” in Proceedingsof the IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, 2004. (MASCOTS '04), pp. 76–83, IEEE, 2004.
  • R. E. Bryant, “Graph-based algorithms for boolean funct ion manipulation,” IEEE Transactions on Computers, vol. C-35, no. 8, pp. 677–691, 1986.
  • H. Tauriainen and K. Heljanko, “Testing LTL formula translation into Büchi automata,” International Journal on Software Tools for Technology Transfer, vol. 4, no. 1, pp. 57–70, 2002. \endinput