The complexity of generalized satisfiability for linear temporal logic

Authors:
Michael Bauland;Thomas Schneider;Henning Schnoor;Ilka Schnoor;Heribert Vollmer
Affiliations:
Theoret. Informatik, Universität Hannover, Hannover, Germany;Informatik, Friedrich-Schiller-Universität, Jena, Germany;Theoret. Informatik, Universität Hannover, Hannover, Germany;Theoret. Informatik, Universität Hannover, Hannover, Germany;Theoret. Informatik, Universität Hannover, Hannover, Germany
Venue:
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Year:
2007

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Abstract

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper undertakes a systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators. Since every propositional operator corresponds to a Boolean function, there exist infinitely many propositional operators. In order to systematically cover all possible sets of them, we use Post's lattice. With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions. Each of these infinitely many problems is shown to be either PSPACE-complete, NP-complete, or in P.