We show that some natural refinements of the Straubing and Brzozowski hierarchies correspond (via the so called leaf-languages) step by step to similar refinements of the polynomial-time hierarchy. This extends a result of Burtschik and Vollmer on relationship between the Straubing and the polynomial hierarchies. In particular, this applies to the Boolean hierarchy and the plus-hierarchy.
@article{ITA_2002__36_1_29_0,
author = {Selivanov, Victor L.},
title = {Relating automata-theoretic hierarchies to complexity-theoretic hierarchies},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {36},
year = {2002},
pages = {29-42},
doi = {10.1051/ita:2002003},
mrnumber = {1928157},
zbl = {1029.03027},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2002__36_1_29_0}
}
Selivanov, Victor L. Relating automata-theoretic hierarchies to complexity-theoretic hierarchies. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) pp. 29-42. doi : 10.1051/ita:2002003. http://gdmltest.u-ga.fr/item/ITA_2002__36_1_29_0/
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