Markov Algorithm Assignment Help

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Markov Algorithm

                  Markov algorithms originally called by their author "normal algorithms" are the result of the attempt by the Russian mathematician A.A Markov to make a rigorous algorithmic process out of the production schemes of E.L post. In a post system one is required to exhibit a sequence of transformation steps or to prove that no such sequence can be found. This is a process which may depend upon a considerable amount of ingenuity or involve non-constructive reasoning which is unsatisfactory from the algorithmic point of view.

                  A Markov algorithm consists of a sequence of pairs-antecedents and consequents which constitute transformation rules to be applied to a string. They are to be tried in the strict priority of the order in which they are listed and the current rule is applied if   the string under transformation contains the antecedent as a substring that being the case the substring found (the first instance in a left to right search) is replaced by the consequent. Furthermore each rule is marked according to whether the process is to be terminated fort with or to be repeated again from the beginning on the transformed string. If no rule applies the process also stops. Thus a quite definite sequence of events is described with which to effect a calculation.

                  A Markov algorithm is a sting rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to have sufficient power to be a general model of computation and can thus be shown to be equivalent in power to a Turing machine. Since this model is Turing-complete, Markov algorithms can represent any mathematical expression from its simple notation.

 

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