Universal turing machine

Turing Formalized concept of computability universal turing machine... 

A universal Turing machine uses an arbitrarily long tape as a potentially infinite memory storage device. Instead, for his proof, Conway used Minsky s idea that a potentially infinite memory can also be obtained by storing arbitrarily large numbers in memory registers. The idea is sketched in figure 3.85. 

A somewhat more robust measure may be defined by invoking the universal Turing machine. Let be the initial state of a computation that is designed to solve a size-N problem. If the problem is to find a solution to the Traveling-Salesman problem, for example, N would correspond to the number of cities that the salesman must visit. 

C. H. Bennett, Logical Depth and Physical Complexity, pp. 227-257 in The Universal Turing Machine A Half Century Survey (Oxford University Press, Oxford, 1988)... 

Alan Turing 1912-1954 UK Universal Turing Machine concept, ACE... 

Bennett, C. H. (1988). Logical depth and physical complexity. In The universal turing machine A half-century survey (pp. 227-257). Available from http //www.springerlink.com/index/HRGl 1848P291274Q.pdf... 

This question has to be framed carefully so that it does not admit trivial solutions (e.g., one can easily design a CA in which Is reproduce themselves)—the automaton in question needs to have a minimal complexity. Von Neumann required that the automaton in question be equivalent in power to a universal Turing machine. 

In this way. Mg simulates any given Turing machine M in real time. As a corollary, a CA Us can be constructed in this way to simulate a universal Turing machine U in real time. (For example, Minsky (1967) described a 6-state, 6-symbol universal Turing machine, so a two-dimensional, 7-state CA can be constructed that simulates it in real time.) In his paper. Smith gives several other variations of the original construction with different number of states, different neighborhood templates, and one-dimensional architectures. 

For both, the switching scheme and Feynman s idea, it is possible to construct universal Turing machines. We will therefore now review an important concept from classical complexity theory concerning universal Turing machines. 

First, in order to apply Peres idea [19] to the Feynman computer, it is necessary to know in advance exactly the time T at which the result is computed. Since this time cannot be predicted by a general algorithm, no universal Turing machine can be constructed with the Peres idea. However, for many calculations we might be able to give reasonable upper time limits, after which we expect the computation to have finished. For the machine described above, since the result is stored safely, we do not have to know the exaet T. 

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