Around Dot-depth One
Formal Languages and Automata Theory
2015-03-19 v1 Logic in Computer Science
Abstract
The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of existential first-order logic without min- or max-predicate. For all fragments, we obtain effective algebraic characterizations. Moreover, we give new combinatorial proofs for the decidability of the membership problem for dot-depth 1/2 and dot-depth 1.
Cite
@article{arxiv.1103.1353,
title = {Around Dot-depth One},
author = {Manfred Kufleitner and Alexander Lauser},
journal= {arXiv preprint arXiv:1103.1353},
year = {2015}
}