Regular languages defined by first-order formulas without quantifier alternation
Logic in Computer Science
2022-08-23 v1 Formal Languages and Automata Theory
Abstract
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments from circuit complexity or algebra. Our proof is much more elementary, and uses only the most basic facts about finite automata.
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Cite
@article{arxiv.2208.10480,
title = {Regular languages defined by first-order formulas without quantifier alternation},
author = {Andreas Krebs and Howard Straubing},
journal= {arXiv preprint arXiv:2208.10480},
year = {2022}
}
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13 pages