Bridging the Gap Between Plain VASS and Branching VASS

2026-09-14

AI Summary

研究解决了BVASS的可达性问题，通过引入新的wqo和利用合并属性，证明了BVASS的可达集与VASS相似，从而推导出关于BVASS可达集几何结构的几个结果。

Abstract

Vectors addition systems with states (VASS), a model equivalent to Petri nets, are finite-state machines with finitely many counters ranging over the natural numbers. The decidable reachability problem for VASS has many applications in logic, automata, and verification. In this paper we study the reachability problem for BVASS, a branching generalization of VASS. We show that BVASS reachability sets are very similar to VASS reachability sets, namely that they are sections of VASS. Our proof relies on a new well-quasi-order (wqo) on BVASS runs that generalizes the well-known wqo on VASS runs. By leveraging an amalgamation property, we prove that every BVASS run can be transformed into an equivalent one of bounded branching complexity. This allows us to derive several results on the geometry of BVASS reachability sets. As an application we obtain that reachability sets of 5-dimensional BVAS are effectively semilinear, as is the case for 5-dimensional VAS.

Problem

• reachability problem
• BVASS
• VASS
• well-quasi-order
• branching complexity

Innovation

• well-quasi-order
• branching VASS
• reachability sets
• amalgamation property
• semilinear