Going higher in the First-order Quantifier Alternation Hierarchy on Words
Formal Languages and Automata Theory
2014-04-29 v1 Logic in Computer Science
Abstract
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a regular language to the levels (boolean combination of formulas having only 1 alternation) and (formulas having only 2 alternations beginning with an existential block). Our proof works by considering a deeper problem, called separation, which, once solved for lower levels, allows us to solve membership for higher levels.
Keywords
Cite
@article{arxiv.1404.6832,
title = {Going higher in the First-order Quantifier Alternation Hierarchy on Words},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1404.6832},
year = {2014}
}