  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.
