Hierarchies and reducibilities on regular languages related to modulo counting

Victor L. Selivanov
2008 RAIRO - Theoretical Informatics and Applications  
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
more » ... n, 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 fatcat:n7kjjgxllzdijp4gu5ub3nbkva