English

Language Equivalence is Undecidable in VASS with Restricted Nondeterminism

Formal Languages and Automata Theory 2025-10-27 v1 Logic in Computer Science

Abstract

In this work, we extend undecidability of language equivalence for two-dimensional Vector Addition System with States (VASS) accepting by coverability condition. We show that the problem is undecidable even when one of the two-dimensional VASSs is deterministic and the other is history-deterministic. Moreover, we observe, that the languages of two history-deterministic VASSs are equal if and only if each can simulate the other. This observation allows us to extend the undecidability to any equivalence relation between two-sided simulation and language equivalence.

Keywords

Cite

@article{arxiv.2510.21514,
  title  = {Language Equivalence is Undecidable in VASS with Restricted Nondeterminism},
  author = {Wojciech Czerwiński and Łukasz Orlikowski},
  journal= {arXiv preprint arXiv:2510.21514},
  year   = {2025}
}