# Going Higher in First-Order Quantifier Alternation Hierarchies on Words

• Published 2017 in ArXiv

#### 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… (More)