Advertisement

A Modal Fixpoint Logic with Chop

  • Markus Müller-Olm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)

Abstract

We study a logic called FLC (Fixpoint Logic with Chop) that extends the modal mu-calculus by a chop-operator and termination formulae. For this purpose formulae are interpreted by predicate transformers instead of predicates. We show that any context-free process can be characterized by an FLC-formula up to bisimulation or simulation. Moreover, we establish the following results: FLC is strictly more expressive than the modal mu-calculus; it is decidable for finite-state processes but undecidable for context-free processes; satisfiability and validity are undecidable; FLC does not have the finite-model property.

Keywords

Model Check Temporal Logic Atomic Proposition Label Transition System Closed Formula 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77–121, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    O. Burkart and J. Esparza. More infinite results. ENTCS, 6, 1997. URL: http://www.elsevier.nl/locate/entcs/volume6.html
  3. 3.
    O. Burkart and B. Steffen. Model checking the full modal mu-calculus for infinite sequential processes. In ICALP’ 97, LNCS 1256, 419–429. Springer-Verlag, 1997.Google Scholar
  4. 4.
    D. Caucal. On the regular structure of prefix rewriting. Theoretical Computer Science, 106:61–86, 1992.CrossRefMathSciNetGoogle Scholar
  5. 5.
    K. Fisler. Containment of regular languages in non-regular timing diagram languages is decidable. In CAV’97, LNCS 1254. Springer-Verlag, 1997.Google Scholar
  6. 6.
    J. F. Groote and H. Hüttel. Undecidable equivalences for basic process algebra. Information and Computation, 115(2):354–371, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.Google Scholar
  8. 8.
    D. Kozen. Results on the propositional mu-calculus. Theoretical Computer Science, 27:333–354, 1983.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Kozen. A finite model theorem for the propositional mu-calculus. Studia Logica, 47:233–241, 1988.CrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Mader. Modal mu-calculus, model checking and Gauss elimination. In TACAS’95, LNCS 1019, 72–88. Springer-Verlag, 1995.Google Scholar
  11. 11.
    R. Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  12. 12.
    F. Moller. Infinite results. In CONCUR’96, LNCS 1119, 195–216. Springer-Verlag, 1996.Google Scholar
  13. 13.
    B. Moszkowski. A temporal logic for multi-level reasoning about hardware. IEEE Computer, 18(2):10–19, 1985.Google Scholar
  14. 14.
    M. Müller-Olm. Derivation of characteristic formulae. ENTCS, 18, 1998. URL: http://www.elsevier.nl/locate/entcs/volume18. html
  15. 15.
    D. M. R. Park. Concurrency and automata on infinite sequences. In LNCS 154, 561–572. Springer-Verlag, 1981.Google Scholar
  16. 16.
    B. Steffen and A. Ingólfsdóttir. Characteristic formulae for processes with divergence. Information and Computation, 110(1):149–163, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Zhou Chaochen, C. A. R. Hoare, and A. P. Ravn. A calculus of durations. Information Processing Letters, 40(5):269–276, 1991.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Markus Müller-Olm
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundDortmundGermany

Personalised recommendations