Parametric Interval Temporal Logic over Infinite Words

TL;DR

This paper introduces parametric HS, a quantitative extension of interval temporal logic over infinite traces, enabling parametric timing constraints, with decidability results and complexity analysis for model checking and satisfiability.

Contribution

It presents the first decidability results for parametric interval temporal logic over infinite traces and identifies a fragment with EXPSPACE-complete complexity.

Findings

Decidability of model checking and satisfiability for PHS.

A fragment of PHS subsuming parametric LTL is EXPSPACE-complete.

Introduction of parametric timing constraints in interval temporal logic.

Abstract

Model checking for Halpern and Shoham's interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics. Here, we focus on the trace-based semantics, where the infinite execution paths (traces) of the given (finite) Kripke structure are the main semantic entities. In this setting, each finite infix of a trace is interpreted as an interval, and a proposition holds over an interval if and only if it holds over each component state (homogeneity assumption). In this paper, we introduce a quantitative extension of HS over traces, called parametric HS (PHS). The novel logic allows to express parametric timing constraints on the duration (length) of the intervals. We show that checking the existence of a parameter valuation for which a Kripke structure satisfies a PHS formula (model checking), or a PHS formula admits a trace as a model under the homogeneity assumption (satisfiability) is decidable. Moreover, we identify a fragment of PHS which subsumes parametric LTL and for which model checking and satisfiability are shown to be EXPSPACE-complete.