Antichains: Alternative Algorithms for LTL Satisfiability and Model-Checking

  • M. De Wulf
  • L. Doyen
  • N. Maquet
  • J. -F. Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4963)


The linear temporal logic (LTL) was introduced by Pnueli as a logic to express properties over the computations of reactive systems. Since this seminal work, there have been a large number of papers that have studied deductive systems and algorithmic methods to reason about the correctness of reactive programs with regard to LTL properties. In this paper, we propose new efficient algorithms for LTL satisfiability and model-checking. Our algorithms do not construct nondeterministic automata from LTL formulas but work directly with alternating automata using efficient exploration techniques based on antichains.


  1. 1.
    Baukus, K., Bensalem, S., Lakhnech, Y., Stahl, K.: Abstracting ws1s systems to verify parameterized networks. In: Schwartzbach, M.I., Graf, S. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 188–203. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: Nusmv: A new symbolic model checker. STTT 2(4), 410–425 (2000)zbMATHGoogle Scholar
  3. 3.
    Clarke, E., Grumberg, O., Hamaguchi, K.: Another look at LTL model checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 415–427. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Daniele, M., Giunchiglia, F., Vardi, M.: Improved automata generation for linear temporal logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 249–260. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    de Alfaro, L., Henzinger, T.A., Majumdar, R.: From verification to control: Dynamic programs for omega-regular objectives. In: LICS, pp. 279–290. IEEE, Los Alamitos (2001)Google Scholar
  6. 6.
    De Wulf, M., 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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Fritz, C.: Constructing Büchi automata from LTL 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
  9. 9.
    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)Google Scholar
  10. 10.
    Gurumurthy, S., Kupferman, O., Somenzi, F., Vardi, M.: On complementing nondeterministic Büchi automata. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 96–110. Springer, Heidelberg (2003)Google Scholar
  11. 11.
    Harding, A.: Symbolic Strategy Synthesis For Games With LTL Winning Conditions. PhD thesis, University of Birmingham (2005)Google Scholar
  12. 12.
    Henzinger, T.A., Kupferman, O., Qadeer, S.: From prehistoric to postmodern symbolic model checking. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 195–206. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Lamport, L.: A new solution of dijkstra’s concurrent programming problem. ACM 17(8), 453–455 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Maquet, N., De Wulf, M., Doyen, L., Raskin, J.-F.: Antichains: Alternative algorithms for LTL satisfiability and model-checking. Technical Report, 84, CFV, Belgium (2008)Google Scholar
  15. 15.
    McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)zbMATHGoogle Scholar
  16. 16.
    Miyano, S., Hayashi, T.: Alternating finite automata on omega-words. In: CAAP, pp. 195–210 (1984)Google Scholar
  17. 17.
    Rohde, S.: Alternating Automata and the Temporal Logic of Ordinals. PhD thesis, University of Illinois at Urbana-Champaign (1997)Google Scholar
  18. 18.
    Rozier, K., Vardi, M.: Ltl satisfiability checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Ruys, T., Holzmann, G.: Advanced Spin tutorial. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 304–305. Springer, Heidelberg (2004)Google Scholar
  20. 20.
    Sebastiani, R., Tonetta, S., Vardi, M.: Symbolic systems, explicit properties: On hybrid approaches for LTL symbolic model checking. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 350–363. Springer, Heidelberg (2005)Google Scholar
  21. 21.
    Somenzi, F.: CUDD: CU Decision Diagram Package, University of Colorado (1998)Google Scholar
  22. 22.
    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
  23. 23.
    Vardi, M.: 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)Google Scholar
  24. 24.
    Vardi, M., Wolper, P.: Reasoning about infinite computations. Information and Computation 115(1), 1–37 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • M. De Wulf
    • 1
  • L. Doyen
    • 2
  • N. Maquet
    • 1
  • J. -F. Raskin
    • 1
  1. 1.CS, Université Libre de Bruxelles (ULB)Belgium
  2. 2.I&C, Ecole Polytechnique Fédérale de Lausanne (EPFL)Switzerland

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