Bauland, Michael and Schneider, Thomas and Schnoor, Henning and Schnoor, Ilka and Vollmer, Heribert - The Complexity of Generalized Satisfiability for Linear Temporal Logic

lmcs:1158 - Logical Methods in Computer Science, January 26, 2009, Volume 5, Issue 1
The Complexity of Generalized Satisfiability for Linear Temporal Logic

Authors: Bauland, Michael and Schneider, Thomas and Schnoor, Henning and Schnoor, Ilka and Vollmer, Heribert

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.


Source : oai:arXiv.org:0812.4848
DOI : 10.2168/LMCS-5(1:1)2009
Volume: Volume 5, Issue 1
Published on: January 26, 2009
Submitted on: March 28, 2008
Keywords: Computer Science - Logic in Computer Science,F.4.1


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