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arXiv · 1707.05696

Going Higher in First-Order Quantifier Alternation Hierarchies on Words

Thomas Place·Marc Zeitoun
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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 $\mathcal{B}{\Sigma}_2$ (finite boolean combinations of formulas having only one alternation) and ${\Sigma}_3$ (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.

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Thomas Place, Marc Zeitoun. 2017-07-15. Going Higher in First-Order Quantifier Alternation Hierarchies on Words. https://arxiv.org/abs/1707.05696

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