Relating automata-theoretic hierarchies to complexity-theoretic hierarchies
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 29-42.

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},
     pages = {29--42},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     doi = {10.1051/ita:2002003},
     zbl = {1029.03027},
     mrnumber = {1928157},
     language = {en},
     url = {http://www.numdam.org/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) no. 1, pp. 29-42. doi : 10.1051/ita:2002003. http://www.numdam.org/item/ITA_2002__36_1_29_0/

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