A Sharper Upper Bound for the Separating Words Problem

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 $O(n^{1/3}\log^7 n)$

Publication Details

Journal
ArXiv.org
Published
2025-03-29
Primary Topic
semigroups and automata theory
Type
article
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article

A Sharper Upper Bound for the Separating Words Problem

ArXiv.org
semigroups and automata theory
article

A Sharper Upper Bound for the Separating Words Problem

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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 $O(n^{1/3}\log^7 n)$

ArXiv.org
Openalex Percentile: Top 49%
semigroups and automata theory
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A Sharper Upper Bound for the Separating Words Problem · ArXiv.org (2025) | TGRS Research Map | TGRS