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Hierarchies and reducibilities on regular languages related to modulo counting

Published online by Cambridge University Press:  15 January 2008

Victor L. Selivanov
Victor L. Selivanov*
Affiliation:
A.P. Ershov Institute of Informatics Systems, Siberian Division of the Russian Academy of Sciences; vseliv@nspu.ru
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Abstract

We discuss some known and introduce some new hierarchies and reducibilities on regular languages, with the emphasis on the quantifier-alternation and difference hierarchies of the quasi-aperiodic languages. The non-collapse of these hierarchies and decidability of some levels are established. Complete sets in the levels of the hierarchies under the polylogtime and some quantifier-free reducibilities are found. Some facts about the corresponding degree structures are established. As an application, we characterize the regular languages whose balanced leaf-language classes are contained in the polynomial hierarchy. For any discussed reducibility we try to give motivations and open questions, in a hope to convince the reader that the study of these reducibilities is interesting for automata theory and computational complexity.

Keywords

Regular languagequasi-aperiodic regular languagequantifier-alternation hierarchydifference hierarchypolylogtime reducibilityquantifier-free reducibilityforbidden pattern.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 95 - 132
Copyright
© EDP Sciences, 2008

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