an oracle machine is an abstract machine used to study decision problems. It can be visualized as a Turing machine with a black box, called an oracle, which...

an oracle Turing machine that, given an oracle for B {\displaystyle B} , computes the characteristic function of A {\displaystyle A} . The Turing jump...

the halting problem for oracle Turing machines running with oracle A. The Turing jump of any set is always of higher Turing degree than the original...

Church's work intertwined with Turing's to form the basis for the Church–Turing thesis. This thesis states that Turing machines, lambda calculus, and other...

computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine that decides...

cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine[citation needed] (devised by...

when there exists an oracle Turing machine which computes some function of P whenever it is given some function from Q as an oracle. Medvedev reducibility...

Turing reducibility. A set A {\displaystyle A} of natural numbers is Turing reducible to a set B {\displaystyle B} if and only if there is an oracle Turing...

super-Turing computation is a set of hypothetical models of computation that can provide outputs that are not Turing-computable. For example, a machine that...

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures...

problem, the Turing jump returns the set of Turing machines that halt when given access to an oracle that solves that problem. The Turing jump of X can...

Turing machine starting from a given state ever print a given symbol?") and to the printing problem considered in Turing's 1936 paper ("does a Turing...

computing, in which Turing machines are augmented with so-called oracles, allowing the study of problems that cannot be solved by Turing machines. John von Neumann...

computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis...

trinary function tripartition Turbo-BM Turbo Reverse Factor Turing machine Turing reduction Turing transducer twin grid file two-dimensional two-level grid...

computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field...

the proof is a string ∈ Σ∗). And the verifier is a randomized oracle Turing Machine V (the verifier) that checks the proof π for the statement that...

purposes). Oracle cloning with improper domain separation breaks security proofs and can lead to successful attacks. According to the Church–Turing thesis...

A set A is computably enumerable with oracle B (or simply "in B") when there is a Turing machine with oracle B which enumerates the members of A; this...

(BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all...

computable functions are the Turing-computable functions and the general recursive functions. According to the Church–Turing thesis, computable functions...

contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical...

Wayback Machine Mitchell, T. (1997). Machine Learning. McGraw Hill. p. 2. ISBN 978-0-07-042807-2. Harnad, Stevan (2008), "The Annotation Game: On Turing (1950)...

its input increases. Per the Church–Turing thesis, any algorithm can be computed by any Turing complete model. Turing completeness only requires four instruction...

problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem. The theorem is named after Stephen...

problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision problem in NP. In other words, a problem X...

science began to converge. In 1980, Paul Benioff introduced the quantum Turing machine, which uses quantum theory to describe a simplified computer. When digital...

formalizations of the concept, a Turing reduction from A to B is a Turing machine augmented with a special instruction "query the oracle". This instruction takes...

that the fundamental conception is owing to Turing—in so far as not anticipated by Babbage.... Both Turing and von Neumann, of course, also made substantial...

given above. If S is a Turing computable set, then both S and its complement are recursively enumerable (if T is a Turing machine giving 1 for inputs in...