Research of options of transition from unlimited to limited parallelism on the example of matrix multiplication

Today, there are many approaches to developing parallel programs. It is considered that it is more efficient to write such programs for a particular computing system. The article proposes to ignore the features of a particular computing system and outline plans for the development of a certain automated system that allows trying to improve code efficiency by developing programs with unlimited parallelism, as well as explore the possibility of developing more efficient programs using the restrictions imposed on maximum parallelism. This approach was demonstrated on the example of the analysis of various matrix multiplication algorithms. As a mathematical apparatus, the study considered various approaches to the description of algorithms to increase their implementation, including an approach based on unlimited parallelism and, also, an approach based on various restrictions on parallelism is proposed. In the course of the work, sequential and parallel methods of matrix multiplication were studied in detail, including tape and block algorithms. As a result of the study, various matrix multiplication methods (sequential, with left and right recursion, parallel methods) were studied and more effective ones were found in terms of the resources used and the restrictions imposed on parallelism. A sequential method and a cascade summation scheme were analyzed and proposed as possible ways of convolving the results of solving the problem obtained after the decomposition stage. Also, a number of programs with different levels of parallelism were developed and implemented in the functional-stream parallel programming language. In the future, such transformations can be carried out formally, relying on a knowledge base and a language that allows equivalent transformations of the original program in accordance with the axioms and algebra of transformations laid down in it, as well as replacing functions that are equivalent in results and have different levels of parallelization. These studies can be used to increase the efficiency of developed programs in terms of resource use in many branches of science, including in the field of software development for the needs of astronomy and rocket science.