A tableau construction for finite linear-time temporal logic

Abstract

This paper gives a tableau-based technique for converting formulas in finite propositional linear-time temporal logic (Finite LTL) into finite-state automata whose languages are the models of the given formula. Finite LTL differs from traditional LTL in that formulas are interpreted with respect to finite, rather than infinite, sequences of states; this fact means that traditional finite-state automata, rather than ω-automata such as those developed by Büchi and others, suffice for recognizing models of such formulas. The approach presented here works by associating with each state in the constructed automaton a Finite LTL formula satisfied by the sequences that can be accepted by the automaton when started in the given state. Such tableau-construction techniques are well-known in the setting of traditional LTL, where they are used to construct ω-automata; we adapt here for the setting of Finite LTL and finite-state automata. The resulting automata may be used as a basis for model checking, model synthesis, query checking and satisfiability testing.