A Mathematical Model of CPU

This paper is based on a previous work of the first author [16] 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 [14], however, it allows for a more realistic modeling of real computers. This new model of computers has been named by the author (Y. Nakamura, [16]) 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 (instruction codes, addresses). The structure of AMI over an arbitrary collection of mathematical domains N consists of: - a non-empty set of objects, - the instruction counter, - a non-empty set of objects called instruction locations, - a non-empty 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 instructio