Applications of information theory to analysis of efficiency and capacity of computers and similar devices

Abstract

We suggest a new approach to definition and estimation of the computer efficiency and the computer capacity. Our definition is based on the analysis of processor instructions and kinds of accessible memory. The suggested approach gives a new look at the construction of computers and similar devices and can be of some interest for practical applications. We consider the problem of what the efficiency and the capacity of a computer are and how they can be estimated. More precisely, we consider a computer with a certain set of instructions and several kinds of memory. What is the computer capacity, if we know the execution time of each instruction and the speed of each kind of memory? What is the computer efficiency if the computer is used for solving problems of a certain kind (say, solving differential equations)? Obviously, the questions about the computer efficiency and capacity are quite natural, but, to the best of our knowledge, the computer science does not give answers to those questions. In this paper, we suggest a definition of the computer efficiency and capacity and methods of their estimation. We also describe a method for estimation of the computer capacity and apply it to several examples which are of some theoretical and practical interest. In particular, this consideration gives a new look at the organization of a computer memory. We will mainly consider computers, but our approach can be applied to all devices which contain processors, memories and instructions. (Among those devices we mention mobile telephones.) The suggested approach is based on methods and ideas of Information Theory, established by C. Shannon.