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if and only if there is an oracle machine that computes the characteristic function of A when run with oracle B. In this case, we also say A is B-recursive and B-computable. If there is an oracle machine that, when run with oracle B, computes a partial function with domain A, then A is said to be B-recursively enumerable and B-computably ...
An oracle machine can be conceived as a Turing machine connected to an oracle. The oracle, in this context, is an entity capable of solving some problem, which for example may be a decision problem or a function problem. The problem does not have to be computable; the oracle is not assumed to be a Turing machine or computer program.
The Turing jump of X can be thought of as an oracle to the halting problem for oracle machines with an oracle for X. [1]Formally, given a set X and a Gödel numbering φ i X of the X-computable functions, the Turing jump X′ of X is defined as
The number of lines needed is 2 n where n is the number of variables. (E. g., with three variables, 2 3 = 8). Start in the right-hand column and alternate T's and F's until you run out of lines. Then move left to the next column and alternate pairs of T's and F's until you run out of lines.
An example of a natural problem in is circuit minimization: given a number k and a circuit A computing a Boolean function f, determine if there is a circuit with at most k gates that computes the same function f. Let C be the set of all boolean circuits. The language
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There is at most one oracle query per deterministic computation step. For the relativized NP oracle, if possible fix the output to be yes by choosing a computation path and fixing the answers of the base oracle; otherwise no fixing is necessary, and either way there is at most 1 answer of the base oracle per step.
The earlier game between these two came down to an Ohio State offensive pass interference penalty that preceded a final play where time expired before a potential game-winning field goal.