The complexity of propositional linear temporal logics in simple cases
It is well-known that model-checking and satisfiability for PLTL are PSPACE-complete. By contrast, very little is known about whether there exist some interesting fragments of PLTL with a lower worst-case complexity. Such results would help understand why PLTL model-checkers are successfully used in practice.
In this paper we investigate this issue and consider model-checking and satisfiability for all fragments of PLTL one obtains when restrictions are put on (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height.
KeywordsModal Logic Temporal Logic Linear Temporal Logic Propositional Variable Atomic Proposition
Unable to display preview. Download preview PDF.
- [DFR97]C. Dixon, M. Fisher, and M. Reynolds. Execution and proof in a Horn-clause temporal logic. In Proc. 2nd Int. Conf. on Temporal Logic (ICTL'97), Manchester, UK, July 1997, 1997. to appear.Google Scholar
- [DS97]S. Demri and Ph. Schnoebelen. The complexity of propositional linear temporal logics in simple cases. Research Report LSV-97-11, Lab. Specification and Verification, ENS de Cachan, Cachan, France, December 1997. Available at http://www.lsv.ens-cachan.fr/tphs. 1Google Scholar
- [EES90]E. A. Emerson, M. Evangelist, and J. Srinivasan. On the limits of efficient temporal decidability. In Proc. 5th IEEE Symp. Logic in Computer Science (LICS'90), Philadelphia, PA, USA, June 1990, pages 464–475, 1990.Google Scholar
- [Eme90]E. A. Emerson. Temporal and modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, vol. B, chapter 16, pages 995–1072. Elsevier Science Publishers, 1990.Google Scholar
- [Joh90]D. S. Johnson. A catalog of complexity classes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, vol. A, chapter 2, pages 67–161. Elsevier Science Publishers, 1990.Google Scholar
- [Lam83]L. Lamport. What good is temporal logic ? In R. E. A. Mason, editor, Information Processing'83. Proc. IFIP 9th World Computer Congress, Sep. 1983, Paris, France, pages 657–668. North-Holland, 1983.Google Scholar
- [MP92]Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, 1992.Google Scholar
- [Spa93]E. Spaan. Complexity Logics. PhD thesis, ILLC, Amsterdam University, NL, March 1993.Google Scholar
- [WVS83]P. Wolper, M. Y. Vardi, and A. P. Sistla. Reasoning about infinite computation paths (extended abstract). In Proc. 24th IEEE Symp. Found. of Computer Science (FOCS'83), Tucson, USA, Nov. 1983, pages 185–194, 1983.Google Scholar