On the random oracle hypothesis
Information and Control
Randomness, relativizations, and polynomial reducibilities
Proc. of the conference on Structure in complexity theory
Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Generic oracles, uniform machines, and codes
Information and Computation
Computability, enumerability, unsolvability
Computability, enumerability, unsolvability
A tight relationship between generic oracles and type-2 complexity theory
Information and Computation
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For each positive integer r, M. Dowd (1992, Inform. and Comput. 96, 65-76) introduced r-generic oracles (we call them r-Dowd oracles; they are different from n-genericity of arithmetical forcing). An oracle D is r -Dowd if every r -query tautology with respect to D is forced by a polynomial-sized portion of D. We propose the study of degrees and complexity of 1-Dowd oracles. Dowd also stated that no r-Dowd oracle is recursively enumerable. However, this is false. We show, among others, the following. There exists a primitive recursive 1-Dowd oracle; For every oracle A, there exists a 1-Dowd oracle D that is Turing-equivalent to A; For every 1-Dowd oracle D, there exists a 1-Dowd oracle E such that E is polynomial time many-one-equivalent to D and E is not 2-Dowd. Problems are formulated, and analogy between the jump-operator and the operation of taking the set of 1-query tautologies is discussed.