English

The Well Structured Problem for Presburger Counter Machines

Formal Languages and Automata Theory 2023-07-11 v2 Logic in Computer Science

Abstract

We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. However, the strong well structured problem is decidable for all Presburger counter machines. While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured problem for 1-Affine VASS.

Cite

@article{arxiv.1910.02736,
  title  = {The Well Structured Problem for Presburger Counter Machines},
  author = {Alain Finkel and Ekanshdeep Gupta},
  journal= {arXiv preprint arXiv:1910.02736},
  year   = {2023}
}

Comments

version 2 of the FSTTCS'2019 paper

R2 v1 2026-06-23T11:36:15.379Z