The Tractability of Model-checking for LTL: The Good, the Bad, and the Ugly Fragments

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

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    In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem 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 systematically studies the model-checking problem for LTL formulae over restricted sets of propositional and temporal operators. For almost all combinations of temporal and propositional operators, we determine whether the model-checking problem is tractable (in P) or intractable (NP-hard). We then focus on the tractable cases, showing that they all are NL-complete or even logspace solvable. This leads to a surprising gap in complexity between tractable and intractable cases. It is worth noting that our analysis covers an infinite set of problems, since there are infinitely many sets of propositional operators. © 2009 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)277-292
    Number of pages15
    JournalElectronic Notes in Theoretical Computer Science
    Issue numberC
    Publication statusPublished - 25 Mar 2009


    • computational complexity
    • linear temporal logic
    • model checking


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