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In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.).
In the Deutsch–Jozsa problem, we are given a black box quantum computer known as an oracle that implements some function: : {,} {,} The function takes n-bit binary values as input and produces either a 0 or a 1 as output for each such value.
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.
Oracle Corporation is an American multinational computer technology company headquartered in Austin, Texas. [5] Co-founded in 1977 by Larry Ellison, who remains executive chairman, Oracle ranked as the third-largest software company in the world by revenue and market capitalization as of 2020, [6] and the company's seat in Forbes Global 2000 was 80 in 2023.
Although the Baker–Gill–Solovay theorem [12] showed that there exists an oracle A such that P A = NP A, subsequent work by Bennett and Gill, [13] showed that for a random oracle B (a function from {0,1} n to {0,1} such that each input element maps to each of 0 or 1 with probability 1/2, independently of the mapping of all other inputs), P B ...
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random).
Definition: We say that is efficiently learnable using in the classification noise model if there exists a learning algorithm that has access to (,) and a polynomial (,,,) such that for any , and it outputs, in a number of calls to the oracle bounded by (,,,, ()), a function that satisfies with probability at least the condition ().
TIBCO Spotfire does not support CTEs, while Oracle 11g Release 2's implementation lacks fixpoint semantics. Without common table expressions or connected-by clauses it is possible to achieve hierarchical queries with user-defined recursive functions. [7]