Geodesic
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

Voir la notice de l'article provenant de la source Numdam

MR Zbl

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
Keywords: regular language, quasi-aperiodic regular language, quantifier-alternation hierarchy, difference hierarchy, polylogtime reducibility, quantifier-free reducibility, forbidden pattern 
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
@article{ITA_2009__43_1_95_0,
     author = {Selivanov, Victor L.},
     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},
     year = {2009},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     doi = {10.1051/ita:2007063},
     mrnumber = {2483446},
     zbl = {1174.03016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2007063/}
}
TY  - JOUR
AU  - Selivanov, Victor L.
TI  - Hierarchies and reducibilities on regular languages related to modulo counting
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2009
SP  - 95
EP  - 132
VL  - 43
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ita:2007063/
DO  - 10.1051/ita:2007063
LA  - en
ID  - ITA_2009__43_1_95_0
ER  - 
%0 Journal Article
%A Selivanov, Victor L.
%T Hierarchies and reducibilities on regular languages related to modulo counting
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2009
%P 95-132
%V 43
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ita:2007063/
%R 10.1051/ita:2007063
%G en
%F ITA_2009__43_1_95_0

Cité par Sources :