Hierarchies and reducibilities on regular languages related to modulo counting
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 95-132.

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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.

DOI : 10.1051/ita:2007063
Classification : 03D05, 03C13, 68Q15
Mots-clés : regular language, quasi-aperiodic regular language, quantifier-alternation hierarchy, difference hierarchy, polylogtime reducibility, quantifier-free reducibility, forbidden pattern 
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     title = {Hierarchies and reducibilities on regular languages related to modulo counting},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {95--132},
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Selivanov, Victor L. Hierarchies and reducibilities on regular languages related to modulo counting. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 95-132. doi : 10.1051/ita:2007063. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007063/

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