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The Turing test, originally called the imitation game by Alan Turing in 1949, [2] is a test of a machine's ability to exhibit intelligent behaviour equivalent to that of a human. In the test, a human evaluator judges a text transcript of a natural-language conversation between a human and a machine. The evaluator tries to identify the machine ...
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
An example: Suppose machine H has tested 13472 numbers and produced 5 satisfactory numbers, i.e. H has converted the numbers 1 through 13472 into S.D's (symbol strings) and passed them to D for test. As a consequence H has tallied 5 satisfactory numbers and run the first one to its 1st "figure", the second to its 2nd figure, the third to its ...
One of the most interesting aspects of the busy beaver game is that, if it were possible to compute the functions Σ(n) and S(n) for all n, then this would resolve all mathematical conjectures which can be encoded in the form "does <this Turing machine> halt". [5] For example, a 27-state Turing machine could check Goldbach's conjecture for each ...
Martin Davis, "What is a computation", in Mathematics Today, Lynn Arthur Steen, Vintage Books (Random House), 1980. A wonderful little paper, perhaps the best ever written about Turing Machines for the non-specialist. Davis reduces the Turing Machine to a far-simpler model based on Post's model of a computation. Discusses Chaitin proof.
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
The success of the Church–Turing thesis prompted variations of the thesis to be proposed. For example, the physical Church–Turing thesis states: "All physically computable functions are Turing-computable." [54]: 101 The Church–Turing thesis says nothing about the efficiency with which one model of computation can simulate another.
With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."