Schöning [14] introduced a notion of helping and suggested the study of the class of the languages that can be helped by oracles in a given class . Later, Ko [12], in order to study the connections between helping and “witness searching”, introduced the notion of self-helping for languages. We extend this notion to classes of languages and show that there exists a self-helping class that we call which contains all the self-helping classes. We introduce the Helping hierarchy whose levels are obtained applying a constant number of times the operator to the set of all the languages. We show that the Helping hierarchy collapses to the -th level if and only if is equal to the -th level. We give characterizations of all the levels and use these to construct a relativized world in which the Helping hierarchy is infinite.
@article{ITA_2001__35_4_367_0,
author = {Cintioli, Patrizio and Silvestri, Riccardo},
title = {The helping hierarchy},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {35},
year = {2001},
pages = {367-377},
mrnumber = {1880805},
zbl = {1052.68050},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2001__35_4_367_0}
}
Cintioli, Patrizio; Silvestri, Riccardo. The helping hierarchy. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) pp. 367-377. http://gdmltest.u-ga.fr/item/ITA_2001__35_4_367_0/
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