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Define a Computational Method [quote]  

2010-11-16 05:19:12|  分类: 默认分类 |  标签: |举报 |字号 订阅

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    A computational method could be defined to be a quadruple in which is a set containing subsets and , and is should leave point wise fixed; that is,should equal for all elements of . The four quantities are intended to represent respectively the states of the computation, the input, the output, and the computation rule. Each input in the set defines a computational sequence, as follows:

    

     and for .

The computational sequence is said to terminate in steps if is the smallest integer for which is in , and in this case it is said to produce the output from . (Note that if is in , so is , because in such a case.) Some computational sequences may never terminate; an algorithm is computational method that terminates in finitely many steps for all in .

The definition above is equivalent to a Turing machine.

 

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