A Tableau Construction for Finite Linear-Time Temporal Logic

TL;DR

This paper introduces a tableau-based method to convert finite propositional linear-time temporal logic formulas into finite-state automata, facilitating model checking and synthesis for finite sequences.

Contribution

It adapts tableau construction techniques from traditional LTL to finite LTL, enabling automata-based analysis for finite sequences.

Findings

Automata accurately represent finite LTL formulas.

Method supports model checking and satisfiability testing.

Automata construction is efficient for finite sequences.

Abstract

This paper describes a method 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 {\omega}-automata such as those developed by B\"uchi and others, suffice for recognizing models of such formulas. The approach considered is based on well-known tableau-construction techniques developed for LTL, which we adapt here for the setting of Finite LTL. The resulting automata may be used as a basis for model checking, satisfiability testing, and model synthesis.