http://worldcat.org/entity/work/id/2242999403

Supportive and parallel-supportive sets

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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