An NP-hardness Result on the Monoid Frobenius Problem
Zhi Xu, J. Shallit
TL;DR
This paper proves that determining whether the Kleene star of a regular expression is not co-finite is an NP-hard problem, highlighting computational complexity challenges in formal language theory.
Contribution
It establishes the NP-hardness of a specific decision problem related to regular expressions and their properties.
Findings
Deciding if $E^*$ is not co-finite is NP-hard.
The result impacts understanding of computational complexity in formal language problems.
Highlights difficulty in analyzing properties of regular expressions.
Abstract
The following problem is NP-hard: given a regular expression , decide if is not co-finite.
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Taxonomy
Topicssemigroups and automata theory · Commutative Algebra and Its Applications · Coding theory and cryptography