A Metric for Linear Temporal Logic

TL;DR

This paper introduces a measure and metric for sets of infinite traces generated by LTL formulas, enabling quantitative analysis of temporal properties using measure theory and SAT-based computation.

Contribution

It presents a novel measure and metric for LTL trace sets, with an implementation leveraging SAT model counting and compositional techniques.

Findings

Efficient computation of measures for bounded LTL properties.

Application of Lebesgue measure to LTL trace sets.

Implementation demonstrates practical feasibility.

Abstract

We propose a measure and a metric on the sets of infinite traces generated by a set of atomic propositions. To compute these quantities, we first map properties to subsets of the real numbers and then take the Lebesgue measure of the resulting sets. We analyze how this measure is computed for Linear Temporal Logic (LTL) formulas. An implementation for computing the measure of bounded LTL properties is provided and explained. This implementation leverages SAT model counting and effects independence checks on subexpressions to compute the measure and metric compositionally.