Revision #1 Authors: Michael Bauland, Thomas Schneider, Henning Schnoor, Ilka Schnoor, Heribert Vollmer

Accepted on: 5th January 2007 00:00

Downloads: 1782

Keywords:

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 PostÃ¢??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.

TR06-153 Authors: Michael Bauland, Thomas Schneider, Henning Schnoor, Ilka Schnoor, Heribert Vollmer

Publication: 15th December 2006 11:10

Downloads: 1982

Keywords:

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 PTIME.