# Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable

LIPICS - Leibniz International Proceedings in Informatics, Feb 2013

We consider the quantifier alternation hierarchy within two-variable first-order logic FO^2[<,suc] over finite words with linear order and binary successor predicate. We give a single identity of omega-terms for each level of this hierarchy. This shows that for a given regular language and a non-negative integer~$m$ it is decidable whether the language is definable by a formula in FO^2[<,suc] which has at most m quantifier alternations. We also consider the alternation hierarchy of unary temporal logic TL[X,F,Y,P] defined by the maximal number of nested negations. This hierarchy coincides with the FO^2[<,suc] quantifier alternation hierarchy.

This is a preview of a remote PDF: http://drops.dagstuhl.de/opus/volltexte/2013/3943/pdf/31.pdf

Manfred Kufleitner, Alexander Lauser. Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable, LIPICS - Leibniz International Proceedings in Informatics, 2013, 305-316, DOI: 10.4230/LIPIcs.STACS.2013.305