Length of the Shortest Word in the Intersection of Regular Languages
Thomas Ang, Jeffrey Shallit
TL;DR
This paper establishes a tight lower bound on the length of the shortest word in the intersection of two regular languages, based on their state complexities, advancing understanding of automata theory.
Contribution
It provides a construction that proves the lower bound of mn-1 for the shortest intersecting word length, which was previously unknown.
Findings
The shortest word length in the intersection can be as large as mn-1.
The bound is tight, meaning it cannot be improved.
The result applies to regular languages with specified state complexities.
Abstract
In this note, we give a construction that provides a tight lower bound of mn-1 for the length of the shortest word in the intersection of two regular languages with state complexities m and n.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · DNA and Biological Computing