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Concept
Markov algorithm
Summary
In theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete, which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation. Markov algorithms are named after the Soviet mathematician Andrey Markov, Jr.
Refal is a programming language based on Markov algorithms.
Normal algorithms are verbal, that is, intended to be applied to strings in different alphabets.
The definition of any normal algorithm consists of two parts: the definition of the alphabet of the algorithm (the algorithm will be applied to strings of these alphabet symbols), and the definition of its scheme. The scheme of a normal algorithm is a finite ordered set of so-called substitution formulas, each of which can be simple or final. Simple substitution formulas are represented by strings of the form , where and are two arbitrary strings in the alphabet of the algorithm (called, respectively, the left and right sides of the formula substitution). Similarly, final substitution formulas are represented by strings of the form , where and are two arbitrary strings in the alphabet of the algorithm. This assumes that the auxiliary characters and do not belong to the alphabet of the algorithm (otherwise two other characters to perform their role as the dividers of the left and right sides, which are not in the algorithm's alphabet, should be selected).
Here is an example of a normal algorithm scheme in the five-letter alphabet :
The process of applying the normal algorithm to an arbitrary string in the alphabet of this algorithm is a discrete sequence of elementary steps, consisting of the following. Let’s assume that is the word obtained in the previous step of the algorithm (or the original word , if the current step is the first). If of the substitution formulas there is no left-hand side which is included in the , then the algorithm terminates, and the result of its work is considered to be the string .
Official source
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