Constraint-based reachability

TL;DR

This paper introduces a constraint-based approach for analyzing reachability in infinite-state imperative programs by modeling program states with constraints, enabling solutions beyond traditional exploration methods.

Contribution

It presents a novel method that interprets filtering consistencies as abstract domain computations to efficiently solve complex reachability problems.

Findings

Constraint-based reachability can handle problems outside traditional exploration scope.

The approach integrates constraint filtering with abstraction techniques.

It produces efficient solutions for previously unsolvable reachability problems.

Abstract

Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with standard backward or forward exploration strategies. An approach that we call Constraint-based reachability, is proposed to address reachability problems by exploring program states using a constraint model of the whole program. The keypoint of the approach is to interpret imperative constructions such as conditionals, loops, array and memory manipulations with the fundamental notion of constraint over a computational domain. By combining constraint filtering and abstraction techniques, Constraint-based reachability is able to solve reachability problems which are usually outside the scope of backward or forward exploration strategies. This paper proposes an interpretation of classical filtering consistencies used in Constraint Programming as abstract domain computations, and shows how this approach can be used to produce a constraint solver that efficiently generates solutions for reachability problems that are unsolvable by other approaches.