Going Higher in First-Order Quantifier Alternation Hierarchies on Words
Logic in Computer Science
2017-07-19 v1
Abstract
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a regular language in the levels (finite boolean combinations of formulas having only one alternation) and (formulas having only two alternations and beginning with an existential block). Our proofs work by considering a deeper problem, called separation, which, once solved for lower levels, allows us to solve membership for higher levels.
Cite
@article{arxiv.1707.05696,
title = {Going Higher in First-Order Quantifier Alternation Hierarchies on Words},
author = {Thomas Place and Marc Zeitoun},
journal= {arXiv preprint arXiv:1707.05696},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1404.6832