A Polynomial-Time Algorithm for Reachability in Branching VASS in Dimension One

TL;DR

This paper proves that reachability, coverability, and boundedness problems in one-dimensional branching VASS are solvable in polynomial time, establishing P-completeness and providing the first decidability results for this subclass.

Contribution

It introduces a polynomial-time algorithm for reachability in one-dimensional BVASS, the first such result for this subclass, and proves P-completeness for coverability and boundedness.

Findings

Reachability in 1D BVASS is P-complete.

Coverability and boundedness in 1D BVASS are P-complete.

First decidability results for this subclass of BVASS.

Abstract

Branching VASS (BVASS) generalise vector addition systems with states by allowing for special branching transitions that can non-deterministically distribute a counter value between two control states. A run of a BVASS consequently becomes a tree, and reachability is to decide whether a given configuration is the root of a reachability tree. This paper shows P-completeness of reachability in BVASS in dimension one, the first decidability result for reachability in a subclass of BVASS known so far. Moreover, we show that coverability and boundedness in BVASS in dimension one are P-complete as well.