Set Theory and Logic

On the Need to Generalize the Theory of Algorithms

Authors: Aleksey A. Demidov
Comments: 13 Pages. In Russian (Correction made by viXra Admin to conform with the rules of viXra.org)

Traditionally, the concept of an algorithm is introduced into the theory through a sequence of elementary steps leading to the solution of a problem, and parallel algorithms are considered as a technical solution external to the Theory of Algorithms, which allows speeding up the execution process. However, a number of physical processes currently used for computing, such as quantum computing, do not fit into the framework of the predictions of the Theory of Algorithms, in particular --- in terms of computational complexity, which suggests that our understanding of parallel computing processes, limited by the framework of the classical Theory of Algorithms, may not be complete. A qualitative leap in the Theory of Computability is possible if parallel algorithms are understood as a generalization of the classical ones within the framework of the hypothetical Theory of Parallel Algorithms. In this paper, pre-quantum physical processes are considered, which are already beyond the scope of the classical Theory of Algorithms. Conceptual primitives suitable for the analysis of parallel flows are proposed.
Category: Set Theory and Logic