Affiliation:
1. Department of Theoretical Computer Science, University of Stuttgart, Universitätsstraβe 38, 70569 Stuttgart, Germany
Abstract
The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider subclasses of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of alternation-free first-order logic without min- or max-predicate, respectively. For all fragments, we obtain effective algebraic characterizations. Moreover, we give new proofs for the decidability of the membership problem for dot-depth 1/2 and dot-depth 1.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Cited by
7 articles.
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1. Dot-depth three, return of the J-class;Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science;2024-07-08
2. Adding Successor;ACM Transactions on Computational Logic;2020-03-18
3. Separability by piecewise testable languages is PTime-complete;Theoretical Computer Science;2018-02
4. The Half-Levels of the FO2 Alternation Hierarchy;Theory of Computing Systems;2016-10-01
5. Stone duality, topological algebra, and recognition;Journal of Pure and Applied Algebra;2016-07