The complexity of generalized satisfiability for linear temporal logic

Michael Bauland, Thomas Schneider, Henning Schnoor, Ilka Schnoor, Heribert Vollmer

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    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 prepositional 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. © Springer-Verlag Berlin Heidelberg 2007.
    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|Lect. Notes Comput. Sci.
    Pages48-62
    Number of pages14
    Volume4423
    Publication statusPublished - 2007
    Event10th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2007 - Braga
    Duration: 1 Jul 2007 → …

    Conference

    Conference10th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2007
    CityBraga
    Period1/07/07 → …

    Keywords

    • Computational complexity
    • Linear temporal logic

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