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 Postâ??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.

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.