# The helping hierarchy

Patrizio Cintioli; Riccardo Silvestri

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

- Volume: 35, Issue: 4, page 367-377
- ISSN: 0988-3754

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topCintioli, Patrizio, and Silvestri, Riccardo. "The helping hierarchy." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.4 (2001): 367-377. <http://eudml.org/doc/92671>.

@article{Cintioli2001,

abstract = {Schöning [14] introduced a notion of helping and suggested the study of the class $\{\rm P\}_\{\rm help\}(\{\mathcal \{C\}\})$ of the languages that can be helped by oracles in a given class $\{\mathcal \{C\}\}$. 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 $\{\rm SH\}$ which contains all the self-helping classes. We introduce the Helping hierarchy whose levels are obtained applying a constant number of times the operator $\{\rm P\}_\{\rm help\}(\cdot )$ to the set of all the languages. We show that the Helping hierarchy collapses to the $k$-th level if and only if $\{\rm SH\}$ 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.},

author = {Cintioli, Patrizio, Silvestri, Riccardo},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

language = {eng},

number = {4},

pages = {367-377},

publisher = {EDP-Sciences},

title = {The helping hierarchy},

url = {http://eudml.org/doc/92671},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Cintioli, Patrizio

AU - Silvestri, Riccardo

TI - The helping hierarchy

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 4

SP - 367

EP - 377

AB - Schöning [14] introduced a notion of helping and suggested the study of the class ${\rm P}_{\rm help}({\mathcal {C}})$ of the languages that can be helped by oracles in a given class ${\mathcal {C}}$. 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 ${\rm SH}$ which contains all the self-helping classes. We introduce the Helping hierarchy whose levels are obtained applying a constant number of times the operator ${\rm P}_{\rm help}(\cdot )$ to the set of all the languages. We show that the Helping hierarchy collapses to the $k$-th level if and only if ${\rm SH}$ 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.

LA - eng

UR - http://eudml.org/doc/92671

ER -

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