Each circle represents a "state" of the table—an "m-configuration" or "instruction". The label e. No general accepted format exists. To the right: the above table as expressed as a "state transition" diagram.

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Introduction[ edit ] Every Turing machine computes a certain fixed partial computable function from the input strings over its alphabet. In that sense it behaves like a computer with a fixed program. However, we can encode the action table of any Turing machine in a string. Thus we can construct a Turing machine that expects on its tape a string describing an action table followed by a string describing the input tape, and computes the tape that the encoded Turing machine would have computed.

Turing described such a construction in complete detail in his paper: "It is possible to invent a single machine which can be used to compute any computable sequence.

If this machine U is supplied with a tape on the beginning of which is written the S. D ["standard description" of an action table] of some computing machine M, then U will compute the same sequence as M.

Davis quotes Time magazine to this effect, that "everyone who taps at a keyboard As the Turing Machine was encouraging the construction of computers , the UTM was encouraging the development of the fledgling computer sciences. An early, if not the very first, assembler was proposed "by a young hot-shot programmer" for the EDVAC Davis Knuth observes that the subroutine return embedded in the program itself rather than in special registers is attributable to von Neumann and Goldstine.

Interpretive routines in the conventional sense were mentioned by John Mauchly in his lectures at the Moore School in Turing took part in this development also; interpretive systems for the Pilot ACE computer were written under his direction" Knuth Davis briefly mentions operating systems and compilers as outcomes of the notion of program-as-data Davis Some, however, might raise issues with this assessment.

At the time mids to mids a relatively small cadre of researchers were intimately involved with the architecture of the new "digital computers". These two aspects of theory and practice have been developed almost entirely independently of each other.

The main reason is undoubtedly that logicians are interested in questions radically different from those with which the applied mathematicians and electrical engineers are primarily concerned. It cannot, however, fail to strike one as rather strange that often the same concepts are expressed by very different terms in the two developments. Minsky goes on to demonstrate Turing equivalence of a counter machine. The names of mathematicians Hermes , , and Kaphenst appear in the bibliographies of both Sheperdson-Sturgis and Elgot-Robinson Two other names of importance are Canadian researchers Melzak and Lambek For much more see Turing machine equivalents ; references can be found at register machine.

Mathematical theory[ edit ] With this encoding of action tables as strings it becomes possible in principle for Turing machines to answer questions about the behaviour of other Turing machines. Most of these questions, however, are undecidable , meaning that the function in question cannot be calculated mechanically. A universal Turing machine can calculate any recursive function , decide any recursive language , and accept any recursively enumerable language. According to the Church—Turing thesis , the problems solvable by a universal Turing machine are exactly those problems solvable by an algorithm or an effective method of computation, for any reasonable definition of those terms.

For these reasons, a universal Turing machine serves as a standard against which to compare computational systems, and a system that can simulate a universal Turing machine is called Turing complete. An abstract version of the universal Turing machine is the universal function , a computable function which can be used to calculate any other computable function.

The UTM theorem proves the existence of such a function. The behavior of a Turing machine M is determined by its transition function. The distinguished states and symbols can be identified by their position, e. Starting from the above encoding, in F.

Hennie and R. Effectively this is an O.

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## Universal Turing machine

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## Teoremas sobre las máquinas de Turing

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