Limitations of the von Neumann architecture computing machine: the numerical nature of computational algorithms

Abstract

Currently, most computing machines have a von Neumann architecture, which has a fundamental limitation: they are exclusively focused on numerical algorithms. The aim of this study is to analyze the numerical nature of computations on von Neumann computers, identify the fundamental limitations associated with this feature, and consider possible ways to overcome them. This study utilizes methods of theoretical analysis of the von Neumann architecture, a review of scientific works in the field of computer engineering and theoretical computer science, and a comparative analysis of classical and alternative computing paradigms. The authors analyze the problems arising when processing non-numeric information within the classical computing paradigm and consider promising directions for overcoming these limitations. The study confirms that the von Neumann architecture is based on the concept of universal computability, where any type of data is represented as numerical sequences. Key limitations of this approach are identified: the lack of semantic interpretation of data, the inability to qualitatively compare heterogeneous quantities, and problems with context. It is shown that some problems are algorithmically intractable on classical computers (for example, the «program halting problem» proved by Turing). Methods for overcoming these limitations are considered: multi-level emulation of non-numerical operations through specially developed numerical algorithms; development of alternative computing paradigms; creation of hybrid computing systems. It is shown that modern computers overcome these limitations through multi-level emulation of non-numerical operations; however, this approach does not solve the fundamental problems. Neuromorphic and quantum computing, memristor systems, and hybrid architectures are considered as promising alternatives. The need to develop new computing paradigms capable of more efficiently processing non-numerical information and solving problems intractable within the classical computing model is substantiated.