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},
pages = {367--377},
year = {2001},
publisher = {EDP Sciences},
volume = {35},
number = {4},
mrnumber = {1880805},
zbl = {1052.68050},
language = {en},
url = {https://www.numdam.org/item/ITA_2001__35_4_367_0/}
}
TY - JOUR AU - Cintioli, Patrizio AU - Silvestri, Riccardo TI - The helping hierarchy JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2001 SP - 367 EP - 377 VL - 35 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/item/ITA_2001__35_4_367_0/ LA - en ID - ITA_2001__35_4_367_0 ER -
%0 Journal Article %A Cintioli, Patrizio %A Silvestri, Riccardo %T The helping hierarchy %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2001 %P 367-377 %V 35 %N 4 %I EDP Sciences %U https://www.numdam.org/item/ITA_2001__35_4_367_0/ %G en %F 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) no. 4, pp. 367-377. https://www.numdam.org/item/ITA_2001__35_4_367_0/
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