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CORR
2008
Springer

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

11 years 5 months ago
The Tractability of Model-Checking for LTL: The Good, the Bad, and the Ugly Fragments
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.
Michael Bauland, Martin Mundhenk, Thomas Schneider
Added 25 Dec 2010
Updated 25 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Michael Bauland, Martin Mundhenk, Thomas Schneider 0002, Henning Schnoor, Ilka Schnoor, Heribert Vollmer
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