RAIRO-Theor. Inf. Appl.
Volume 35, Number 4, July/August 2001
|Page(s)||367 - 377|
|Published online||15 April 2002|
The Helping Hierarchy
Dipartimento di Matematica e Fisica,
Università di Camerino, Via Madonna delle Carceri, 62032 Camerino
(MC), Italy; (firstname.lastname@example.org)
2 Dipartimento di Scienze dell'Informazione, Università di Roma "La Sapienza" , Via Salaria 113, 00198 Roma, Italy; (email@example.com)
Accepted: November 2001
Schöning  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 , 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 SH 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 k-th level if and only if SH is equal to the k-th level. We give characterizations of all the levels and use these to construct a relativized world in which the Helping hierarchy is infinite.
Mathematics Subject Classification: 68Q15 / 68Q05 / 03D15
© EDP Sciences, 2001
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