Université Catholique de Louvain A Mathematical Model of CPU Yatsuka Nakamura.pdf

FORMALIZED MATHEMATICS Volume 3, Number 2, 1992 Universit´e Catholique de Louvain A Mathematical Model of CPU Yatsuka Nakamura Andrzej Trybulec1 Shinshu University Warsaw University Nagano Bialystok Summary. This paper is based on a previous work of the first author [12] in which a mathematical model of the computer has been presented. The model deals with random access memory, such as RASP of C. C. Elgot and A. Robinson [11], however, it allows for a more re alistic modeling of real computers. This new model of computers has been named by the author (Y. Nakamura, [12]) Architecture Model for Instructions (AMI). It is more developed than previous models, both in the description of hardware (e.g., the concept of the program counter, the structure of memory) as well as in the description of instructions (instruc tion codes, addresses). The structure of AMI over an arbitrary collection of mathematical domains N consists of: a nonempty set of objects, the instruction counter, a nonempty set of objects called instruction locations, a nonempty set of instruction codes, an instruction code for halting, a set of instructions that are ordered pairs with the first element being an instruction code and the second a finite sequence in which members are either objects of the AMI or elements of one of the domains included in N, a function that assigns to every object of AMI its kind that is either an instruction or an instruction location or an e