Model Checking Flat Freeze LTL on One-Counter Automata

TL;DR

This paper proves the decidability of model checking flat Freeze LTL on one-counter automata by reducing it to a reachability problem and translating it into Presburger arithmetic, resolving an open problem.

Contribution

It demonstrates that model checking flat Freeze LTL on one-counter automata is decidable, using a reduction to reachability and Presburger arithmetic translation.

Findings

Decidability of model checking flat Freeze LTL on one-counter automata.

Reduction of the problem to reachability with parameterised tests.

Translation of reachability problem into Presburger arithmetic.

Abstract

Freeze LTL is a temporal logic with registers that is suitable for specifying properties of data words. In this paper we study the model checking problem for Freeze LTL on one-counter automata. This problem is known to be undecidable in general and PSPACE-complete for the special case of deterministic one-counter automata. Several years ago, Demri and Sangnier investigated the model checking problem for the flat fragment of Freeze LTL on several classes of counter automata and posed the decidability of model checking flat Freeze LTL on one-counter automata as an open problem. In this paper we resolve this problem positively, utilising a known reduction to a reachability problem on one-counter automata with parameterised equality and disequality tests. Our main technical contribution is to show decidability of the latter problem by translation to Presburger arithmetic.