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You will learn the basics of preparing the thesis as well as fundamentals of Computer Science.The full guide for publishing your research is also given.This work describes the hypothesis of the relation between the classes of complexity: for this purpose we define the functions over algorithms or state machines for which the equality holds true and, thus, the decision can be made towards polynomial reduction of the computational complexity of algorithms. The specific class of impractical or exponential measures of complexity against the polynomial ones is also discussed - for this case we divide these classes according to the discrete numbers which are known to the present time. We also present the approximate algorithm for the classical NP-complete problem like Traveling Salesman using the memory construction. The question of P and NP equality is important in decision-making algorithms which commonly decide inequality of these classes - we define the memory factor which is exponential and space consumption is non-deterministic. The memory consumption problem within the memorization principle or dynamic programming can be of varying nature giving us the decision to build the approximation methods like it's shown on the example of Traveling Salesman problem. We also give the notion of the past work in theory of complexity which, in our opinion, is of the same consideration in most cases when the functional part is omitted or even isn't taken into account. The model theorem with its proof of the equality of classes over congruent function is also given in the end of this article.In this continued series of work, we present the theoretical and practical results towards reasoning with modern methods of Artificial Intelligence (AI). We justify our methodology with help of illustrative examples from Computer Science relying on the regular expression matching algorithm and application of the proposed solution for the task of identifying files consistency according to the unknown format. We will also give several notable proofs to the classical theorems which in some sense are coherent to the terms like AI and algorithmic complexity, however, or at least, nowadays they're solved involving the huge amount of hardware resources and together constitute the new formation in the modern age with help of specifically crafter hardware modules - we're still about to represent the model in more classical understanding from the point of view of computational complexity, concise reasoning and computer logic within the classical models, theorems and proofs as the base approach of estimating the costs needed to build Artificial Neural Networks (ANN) or Machine Learning (ML) data.

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