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What is the general strategy for Markov Algorithm?

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The general strategy in a Markov Algorithm is to take as input a string x and, through a number of steps in the algorithm, transform x to an output string y. this transformation process is generally performed in computers for text editing or program compilation.

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The most basic tool used to express generating functions in closed form is the closed form expression for the geometric series, which is an expression of the form a+ar+ar2+-------+arn. It can either be terminated or extended indefinitely. What are the restrictions for this geometric series?What are the two ways through which the Markov algorithm terminates?