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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).
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 machine cannot be the subject of its own thought (or can't be self-aware). A program which can report on its internal states and processes, in the simple sense of a debugger program, can certainly be written. Turing asserts "a machine can undoubtably be its own subject matter." A machine cannot have much diversity of behaviour. He notes that ...
A Turing machine that "solves" a problem is generally meant to mean one that decides the language. Turing machines enable intuitive notions of "time" and "space". The time complexity of a TM on a particular input is the number of elementary steps that the Turing machine takes to reach either an accept or reject state.
In computability theory, the Church–Turing thesis (also known as computability thesis, [ 1 ] the Turing–Church thesis, [ 2 ] the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an ...
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:
Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. [ a ] A related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. [citation needed] The Church–Turing ...
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 ...