A Modal Fixpoint Logic with Chop
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.
KeywordsModel Check Temporal Logic Atomic Proposition Label Transition System Closed Formula
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- 2.O. Burkart and J. Esparza. More infinite results. ENTCS, 6, 1997. URL: http://www.elsevier.nl/locate/entcs/volume6.html
- 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
- 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
- 7.J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.Google Scholar
- 10.A. Mader. Modal mu-calculus, model checking and Gauss elimination. In TACAS’95, LNCS 1019, 72–88. Springer-Verlag, 1995.Google Scholar
- 11.R. Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
- 12.F. Moller. Infinite results. In CONCUR’96, LNCS 1119, 195–216. Springer-Verlag, 1996.Google Scholar
- 13.B. Moszkowski. A temporal logic for multi-level reasoning about hardware. IEEE Computer, 18(2):10–19, 1985.Google Scholar
- 14.M. Müller-Olm. Derivation of characteristic formulae. ENTCS, 18, 1998. URL: http://www.elsevier.nl/locate/entcs/volume18. html
- 15.D. M. R. Park. Concurrency and automata on infinite sequences. In LNCS 154, 561–572. Springer-Verlag, 1981.Google Scholar