Solving the Reachability Problem for Branching Vector Addition Systems via Semilinear Inductive Invariants

2026-07-10

AI Summary

This work resolves the long-standing reachability problem for Branching Vector Addition Systems (BVAS). The central contribution is the first proof that for any unreachable configuration, there exists a semilinear inductive invariant excluding it. Building on this theoretical result, the authors reduce reachability verification to an enumerable search problem. By integrating insights from the theory of semilinear sets and inductive invariants, they devise a concise and efficient enumeration algorithm that fully decides BVAS reachability.

Abstract

In this paper, we solve the reachability problem for branching vector addition systems (BVAS), a long standing open problem. Our approach is based on semilinear inductive invariants. More precisely, we prove that if a configuration of a BVAS is not reachable, then there exists an inductive invariant, given as a semilinear set, that does not contain this configuration. Based on this property, we deduce a very simple (enumerative) algorithm solving the reachability problem for BVAS.

Problem

• reachability problem
• branching vector addition systems
• BVAS
• semilinear inductive invariants

Innovation

• branching vector addition systems
• reachability problem
• semilinear inductive invariants
• enumerative algorithm