On the Coverability Problem for Pushdown Vector Addition Systems in One Dimension

TL;DR

This paper proves the decidability of the coverability problem for one-dimensional pushdown vector addition systems by analyzing a new model called grammar-controlled vector addition systems, addressing key verification challenges.

Contribution

It introduces the concept of grammar-controlled vector addition systems and establishes their role in solving the coverability problem for one-dimensional pushdown VAS.

Findings

Decidability of coverability in one-dimensional pushdown VAS.

Introduction of grammar-controlled vector addition systems.

Framework for verifying recursive programs with integer parameters.

Abstract

Does the trace language of a given vector addition system (VAS) intersect with a given context-free language? This question lies at the heart of several verification questions involving recursive programs with integer parameters. In particular, it is equivalent to the coverability problem for VAS that operate on a pushdown stack. We show decidability in dimension one, based on an analysis of a new model called grammar-controlled vector addition systems.