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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).
The Automatic Computing Engine (ACE) was a British early electronic serial stored-program computer design by Alan Turing. Turing completed the ambitious design in late 1945, having had experience in the years prior with the secret Colossus computer at Bletchley Park. The ACE was not built, but a smaller version, the Pilot ACE, was constructed ...
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
A simple generalization is the extension to Turing machines with m symbols instead of just 2 (0 and 1). [10] For example a trinary Turing machine with m = 3 symbols would have the symbols 0, 1, and 2. The generalization to Turing machines with n states and m symbols defines the following generalized busy beaver functions:
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal model of computation that can be used to simulate any Turing machine (and vice ...
The Z3 was demonstrated in 1998 to be, in principle, Turing-complete. [13] However, because it lacked conditional branching, the Z3 only meets this definition by speculatively computing all possible outcomes of a calculation. Thanks to this machine and its predecessors, Konrad Zuse has often been suggested as the inventor of the computer.
Formal definitions. [] In computability theory, several closely related terms are used to describe the computational power of a computational system (such as an abstract machine or programming language): Turing completeness. A computational system that can compute every Turing- computable function is called Turing-complete (or Turing-powerful).
Halting problem. hide. In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for ...