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Enhancing Simulation for Checking Language Containment

  • Jin Yi
  • Wenhui Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

Many verification approaches based on automata theory are related to the language containment problem, which is PSPACE-complete for nondeterministic automata. To avoid such a complexity, one may use simulation as an approximation to language containment, since simulation implies language containment and computing simulation is a polynomial time problem. As it is an approximation, there exists a gap between simulation and language containment, therefore there has been an effort to develop methods to narrow the gap while keeping the computation in polynomial time. In this paper, we present such an approach by building a Büchi  automaton based on partial marked subset construction to be used in the computation of simulation relation, such that the automaton preserves the original language and has a structure that helps identify more pairs of automata that are in language containment relation. This approach is an improvement to the fair-k-simulation method [3].

Keywords

Transition Relation Linear Temporal Logic Original Language Automaton Theory Tree Automaton 
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.

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References

  1. 1.
    Bustan, D., Grumberg, O.: Applicability of fair simulation. Information and computation 194(1), 1–18 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dill, D.L., Hu, A.J., Wong-Toi, H.: Checking for language inclusion using simulation preorders. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 255–265. Springer, Heidelberg (1992)Google Scholar
  3. 3.
    Etessami, K.: A Hierarchy of Polynomial-Time Computable Simulations for Automata. In: Brim, L., et al. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 131–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Holzmann, G.J., Etessami, K.: Optimizing Büchi Automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)Google Scholar
  5. 5.
    Etessami, K., Wilke, T., Schuller, R.: Fair simulation relations, parity games, and state space reduction for Büchi automata. SIAM Journal of Computing 34(5), 1159–1175 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fritz, C.: Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata. In: H. Ibarra, O., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 35–48. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Gurumurthy, S., Bloem, R., Somenzi, F.: Fair Simulation Minimization. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 610–624. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    Henzinger, T.A., Kupferman, O., Rajamani, S.K.: Fair simulation. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 273–287. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Jurdzinski, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Kesten, Y., Piterman, N., Pnueli, A.: Bridging the Gap Between Fair Simulation and Trace Inclusion. Information and Computation 200(1), 35–61 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. In: STOC’98, pp. 408–429 (1998)Google Scholar
  13. 13.
    Lindahl, A.: Complementation of Büchi automata: A survey and implementation. Master thesis, Linköpings university Department of computer and information science (2004)Google Scholar
  14. 14.
    Miyano, S., Hayashi, T.: Alternating Finite Automata on ω-Words. Theoretical Computer Science 32, 321–330 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  16. 16.
    Mukund, M.: Finite-state Automata on Infinte Inputs. In: Sixth National Seminar on Theoretical Computer Science, Banasthali Vidyapith, Banasthali, Rajasthan (1996)Google Scholar
  17. 17.
    Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM Journal of Research 3(2), 115–125 (1959)MathSciNetGoogle Scholar
  18. 18.
    Safra, S.: Complexity of automata on infinite object. PhD thesis (1989)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jin Yi
    • 1
    • 2
  • Wenhui Zhang
    • 1
  1. 1.Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, BeijingChina
  2. 2.Graduate University of the Chinese Academy of Sciences, BeijingChina

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