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Theory of Computation:
Presumably, the first algorithm designed was an unusual addition thousands of years ago to another cave. Lamble bone type devices are used to perform that process. The concept of algorithm is very well developed in Euclid school. Two amazing examples are: Euclidean Algorithm for calculating GCD.
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It is a non-trivial algorithm, in the sense that it is not at all clear why it counts GCD. The construction of a compass ruler is an example of an accurate algorithms. The first steps are well defined and the tasks are well defined. Turing Machines and Algorithms Fortunately the mathematical concept of which algorithm and calculation was already developed by Mataysavich.
CS701 Theory of Computation:
counting. Algorithms and calculations The seed of the answer to this question was also sown by Hilbert. In 1928, Hilbert, who wanted to compile the statistics, had filed a complaint with the Entscheidungs. He was looking for an algorithm that would take mathematical certainty and determine if what was said was true or not.
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Turing machine is a mathematical model that describes an invisible machine that changes the signals in a tape line according to the rules table. Despite the simplicity of the model, it is able to use any computer algorithm.
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Then, based on the symbol and current state of the machine, the machine writes the symbol in the same cell, and moves the head one step left or right,  or stop counting. The choice of which changing sign to be written and which direction to go is based on a rated table that specifies what should be done with each combination of current status and the symbol being read.
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The machine works on an endless memory cassette that is divided into different cells, each of which can hold a single symbol drawn from a limited set of symbols called the machine alphabet. It has a “head” which, at any time in the operation of the machine, is placed on one of these cells.