Tableau-based automata construction for dynamic linear time temporal logic*

Article

We present a tableau-based algorithm for obtaining a Büchi automaton from a formula in Dynamic Linear Time Temporal Logic (DLTL), a logic which extends LTL by indexing the until operator with regular programs. The construction of the states of the automaton is similar to the standard construction for LTL, but a different technique must be used to verify the fulfillment of until formulas. The resulting automaton is a Büchi automaton rather than a generalized one. The construction can be done on-the-fly, while checking for the emptiness of the automaton. We also extend the construction to the Product Version of DLTL.

Keywords

temporal logic model checking 

AMS subject classification

03B44 68N30 

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References

  1. [1]
    F. Bacchus and F. Kabanza, Planning for temporally extended goals, Annals of Mathematics and Artificial Intelligence 22 (1998) 5–27.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    D. Calvanese, G. De Giacomo and M.Y. Vardi, Reasoning about actions and planning in LTL action theories, in: Proc. Principles of Knowledge Representation and Reasoning, KR'02, (Morgan Kaufmann, 2002) pp. 593–602.Google Scholar
  3. [3]
    M. Daniele, F. Giunchiglia and M.Y. Vardi, Improved automata generation for linear temporal logic, in: Proc. Computer Aided Verification, 11th International Conference, CAV'99, Lecture Notes in Computer Science, Vol. 1633 (Springer, 1999) pp. 249–260.Google Scholar
  4. [4]
    R. Gerth, D. Peled, M.Y. Vardi and P. Wolper, Simple on-the-fly automatic verification of linear temporal logic, in: Proc. 15th International Symposium on Protocol Specification, Testing and Verification XV, PSTV 1995 (IFIP Conference Proceedings 38 Chapman & Hall, 1996) pp. 3–18.Google Scholar
  5. [5]
    L. Giordano, A. Martelli and C. Schwind, Reasoning about actions in dynamic linear time temporal logic, Logic Journal of the IGPL 9(2) (2001) 289–303.CrossRefMathSciNetGoogle Scholar
  6. [6]
    L. Giordano, A. Martelli and C. Schwind, Specifying and verifying systems of communicating agents in a temporal action logic, in: Proc. AI*IA 2003: Advances in Artificial Intelligence, 8th Congress of the Italian Association for Artificial Intelligence, Lecture Notes in Computer Science, Vol. 2829 (Springer, 2003) pp. 262–274.Google Scholar
  7. [7]
    L. Giordano, A. Martelli and C. Schwind, Verifying communicating agents by model checking in a temporal action logic, in: Proc. Logics in Artificial Intelligence, 9th European Conference, JELIA 2004, Lecture Notes in Computer Science, Vol. 3229 (Springer, 2004) pp. 57–69.Google Scholar
  8. [8]
    F. Giunchiglia and P. Traverso, Planning as model checking, in: Proc. The 5th European Conference on Planning, ECP'99, Lecture Notes in Computer Science, Vol. 1809 (Springer, 2000) pp. 1–20.Google Scholar
  9. [9]
    J.G. Henriksen and P.S. Thiagarajan, A product version of dynamic linear time temporal logic, in: Proc. CONCUR '97: Concurrency Theory, 8th International Conference, Lecture Notes in Computer Science, Vol. 1243 (Springer, 1997) pp. 45–58.Google Scholar
  10. [10]
    J.G. Henriksen and P.S. Thiagarajan, Dynamic linear time temporal logic, Annals of Pure and Applied Logic 96(1–3) (1999) 187–207.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    G.J. Holzmann, The model checker SPIN, IEEE Transaction on Software Engineering 23(5) (1997) 279–295.CrossRefMathSciNetGoogle Scholar
  12. [12]
    J. Hromkovic, S. Seibert and T. Wilke, Translating regular expressions into small ɛ-free nondeterministic finite automata, in: Proc. STACS 97, 14th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 1200 (Springer, 1997) pp. 55–66.Google Scholar
  13. [13]
    W. Penczek and A. Lomuscio, Verifying epistemic properties of multi-agent systems via bounded model checking, Fundamenta Informaticae 55(2) (2003) 167–185.MATHMathSciNetGoogle Scholar
  14. [14]
    M. Pistore and P. Traverso, Planning as model checking for extended goals in non-deterministic domains, in: Proc. of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001 (Morgan Kaufmann, 2001) pp.479–484.Google Scholar
  15. [15]
    R. Reiter, The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, ed. V. Lifschitz (Academic, 1991) pp. 359–380.Google Scholar
  16. [16]
    M.P. Singh, Agent communication languages: Rethinking the principles, IEEE Computer 31(12) (1998) 40–47.Google Scholar
  17. [17]
    A.P. Sistla and E.M. Clarke, The complexity of propositional linear temporal logic, Journal of the ACM 32 (1985) 733–749.CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    R.G. Smith, The contract net protocol: High level communication and control in a distributed problem solver, IEEE Transactions on Computers C-29(12) (1980) 1104–1113.CrossRefGoogle Scholar
  19. [19]
    F. Somenzi and R. Bloem, Efficient Büchi automata from LTL formulae, in: Proc. Computer Aided Verification, 12th International Conference, CAV 2000, Lecture Notes in Computer Science, Vol. 1855 (Springer, 2000) pp. 247–263.Google Scholar
  20. [20]
    W. van der Hoek and M.J.W. Wooldridge, Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications, Studia Logica 75(1) (2003) 125–157.CrossRefMATHMathSciNetGoogle Scholar
  21. [21]
    M. Vardi and P. Wolper, Reasoning about infinite computations, Information and Computation 115 (1994) 1–37.CrossRefMATHMathSciNetGoogle Scholar
  22. [22]
    M. Wooldridge, M. Fisher, M.P. Huget and S. Parsons, Model checking multi-agent systems with MABLE, in: Proc. First International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2002 (ACM, 2002) pp. 952–959.Google Scholar
  23. [23]
    P. Wolper, Temporal logic can be more expressive, Information and Control 56 (1983) 72–99.CrossRefMATHMathSciNetGoogle Scholar
  24. [24]
    P. Wolper, Constructing automata from temporal logic formulas: A tutorial, in: Lectures on Formal Methods and Performance Analysis FMPA 2000, Lecture Notes in Computer Science, Vol. 2090 (Springer, 2001) pp. 261–277.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità del Piemonte OrientaleAlessandriaItaly
  2. 2.Dipartimento di InformaticaUniversità di TorinoTorinoItaly

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