The complexity of bidirected reachability in valence systems

TL;DR

This paper investigates the complexity of reachability in bidirected valence systems, showing that for many storage mechanisms, the problem becomes significantly easier, often polynomial time, compared to general reachability.

Contribution

It provides a comprehensive complexity analysis of bidirected reachability in valence systems, revealing complexity reductions across various storage models.

Findings

Complexity drops to polynomial time for many storage mechanisms.

Bidirected systems allow more efficient reachability analysis.

The framework models counters, pushdowns, and combinations effectively.

Abstract

Reachability problems in infinite-state systems are often subject to extremely high complexity. This motivates the investigation of efficient overapproximations, where we add transitions to obtain a system in which reachability can be decided more efficiently. We consider bidirected infinite-state systems, where for every transition there is a transition with opposite effect. We study bidirected reachability in the framework of valence systems, an abstract model featuring finitely many control states and an infinite-state storage that is specified by a finite graph. By picking suitable graphs, valence systems can uniformly model counters as in vector addition systems, pushdowns, integer counters, and combinations thereof. We provide a comprehensive complexity landscape for bidirected reachability and show that the complexity drops (often to polynomial time) from that of general reachability, for almost every storage mechanism where reachability is known to be decidable.