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arXiv · 2510.21514

Language Equivalence is Undecidable in VASS with Restricted Nondeterminism

Wojciech Czerwiński·Łukasz Orlikowski
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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.

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Wojciech Czerwiński, Łukasz Orlikowski. 2025-10-24. Language Equivalence is Undecidable in VASS with Restricted Nondeterminism. https://arxiv.org/abs/2510.21514

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