A Sharper Upper Bound for the Separating Words Problem

Bogdan C. Dumitru

A Sharper Upper Bound for the Separating Words Problem

Formal Languages and Automata Theory 2025-04-03 v2 Number Theory

Authors: Bogdan C. Dumitru

Abstract

We show that for any two distinct words $s_1, s_2$ over an arbitrary alphabets, there exists a deterministic finite automaton with $O(\log^2 n)$ states that accepts $s_1$ and rejects $s_2$ . This improves the previous upper bound of $O(n^{1/3}\log^7 n)$

Keywords

automata theory computational complexity first-order logic

Cite

@article{arxiv.2503.23184,
  title  = {A Sharper Upper Bound for the Separating Words Problem},
  author = {Bogdan C. Dumitru},
  journal= {arXiv preprint arXiv:2503.23184},
  year   = {2025}
}

Comments

An error has been identified in the proof of Theorem 1. Correcting the argument presented yields an upper bound which does not improve upon existing results (e.g., [Chase 2020]), so this paper does not in fact provide an improved upper bound. We therefore withdraw our claim of a stronger result

A Sharper Upper Bound for the Separating Words Problem

Abstract

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