A.1型文法B.2型文法C.3型文法D.0型文法
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Every Turing machine computes a certain(74)partial function over the strings over its alphabet. In that sense it behaves like a computer with a fixed program. However, as Alan luring already described, we can encode the action table of every Turing machine in a string. Thus we might try to construct a Turing machine that expects on its tape a string describing an action table followed by a string describing the input tape, and then computes the tape that the encoded Turing machine would have computed. As Turing showed, such a luring machine is indeed possible and since it is able to simulate any other Turing machine it is called a(75)Turing machine.
A universal Turing machine is Turing complete. It 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.
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