Abstract
We address the problem of estimating the efficiency and capacity of computers. The main goal of our approach is to give a method for comparing the capacity of different computers, which can have different sets of instructions, different kinds of memory, a different number of cores (or processors), etc. We define efficiency and capacity of computers and suggest a method for their estimation, which is based on the analysis of processor instructions and their execution time. How the suggested method can be applied to estimate the computer capacity is shown. In particular, this consideration gives a new look at the organization of the memory of a computer. Obtained results can be of some interest for practical applications.
Highlights
Nowadays, computer science includes many natural approaches and models which give a possibility to estimate the power of different computational models and the complexity of different computational tasks
Much less is known about how to compare the performance of real computers that can have different clock rates, different sets of instructions, different kinds of memory, different number of cores, etc
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 and routers.) Besides, we describe a method for estimating the computer capacity and apply it to several examples which are of some theoretical and practical interest
Summary
Computer science includes many natural approaches and models which give a possibility to estimate the power of different computational models and the complexity of different computational tasks. (Here and below T is an integer, log x ≡ log x and |Y | is the number of elements of Y if Y is a set, and the length of Y if Y is a word.) In other words, the total number of computer tasks executed in time T is equal to (1) Basing on this consideration we give the following definition. Definition 2 Let there be a computer with a set of instructions I and let τ (x) be the execution time of an instruction x ∈ I Let this computer be used for solving such a randomly generated sequence of computer tasks, that the corresponding sequence of the instructions z = z1 z2 ..., zi ∈ I, is a stationary ergodic stochastic process. We do not give it, because definitions do not need to be proven, but mention that there are many results about channels which transmit letters of unequal duration [8]
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