English

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.

Keywords

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}
}

Comments

13 pages

R2 v1 2026-06-25T01:52:50.720Z