Affiliation:
1. Wilhelm-Schickard-Institut, Universität Tübingen, Germany
2. Computer Science Department, Boston College, Massachusetts, USA
Abstract
We give an algebraic characterization, based on the bilateral semidirect product of finite monoids, of the quantifier alternation hierarchy in two-variable first-order logic on finite words. As a consequence, we obtain a new proof that this hierarchy is strict. Moreover, by application of the theory of finite categories, we are able to make our characterization effective: that is, there is an algorithm for determining the exact quantifier alternation depth for a given language definable in two-variable logic.
Funder
DFG Emmy-Noether program KR
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
3 articles.
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