Computing All Facts Entailed By An LTL Specification

We study the problem of efficiently computing all (usually infinitely many) facts which are entailed by a specification written in linear temporal logic (LTL)-a standard formalism for specifying and verifying properties of computations in reactive systems. This problem can be seen as a generalisation of the standard entailment checking, but whose output provides a much wider understanding of the system’s behaviour. We show that in full LTL the problem can be solved in doubly exponential time, whereas for Horn fragments of LTL, which can be seen as temporal logic programs, the problem can be solved in exponential or only quadratic time, depending on the allowed temporal operators in the input formula. Moreover, we show that all these bounds are optimal. We also implement and experimentally compare two techniques for solving the problem: an automata-based algorithm for full LTL and a materialisation-based algorithm for Horn fragments. The obtained results suggest practical usefulness of our approach.