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Supportive and parallel-supportive sets

Author: Richard Beigel; William I Gasarch
Publisher: College Park, Md. : University of Maryland, 1987.
Series: University of Maryland at College Park.; Computer science technical report series
Edition/Format:   Book : English
Database:WorldCat
Summary:
Abstract: "Let A be an oracle. We say that A is supportive if we can solve more decision problems by making n+1 queries to A than we can solve by making only n queries to A. We say that A is parallel-supportive if we can solve more decision problems by making n+1 simultaneous queries to A than we can solve by making only n simultaneous queries to A. We conjecture that all nonrecursive sets are supportive. In [BGH87]  Read more...
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Document Type: Book
All Authors / Contributors: Richard Beigel; William I Gasarch
OCLC Number: 21101617
Notes: "March 28, 1987."
Description: 19 pages ; 28 cm.
Series Title: University of Maryland at College Park.; Computer science technical report series
Responsibility: Richard Beigel, William I. Gasarch.

Abstract:

Abstract: "Let A be an oracle. We say that A is supportive if we can solve more decision problems by making n+1 queries to A than we can solve by making only n queries to A. We say that A is parallel-supportive if we can solve more decision problems by making n+1 simultaneous queries to A than we can solve by making only n simultaneous queries to A. We conjecture that all nonrecursive sets are supportive. In [BGH87] we showed that the halting set is supportive and parallel supportive. In this paper we show that the jump of every set is supportive and parallel supportive, all generic sets are supportive and parallel-supportive, all semi-recursive sets are supportive and parallel-supportive, every Turing degree contains a set that is supportive and parallel supportive, and every r.e. Turing degree contains an r.e. set that is supportive and parallel-supportive. We also show that the jump of every Turing degree contains a set that is not parallel supportive."

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