Introduction to Mathematical Machine Theory
Introduction to Mathematical Machine Theory
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ICFEM'07 Proceedings of the formal engineering methods 9th international conference on Formal methods and software engineering
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A computer is a set M (the memory), a set B, a class of maps S: M → B, known as states, and a class @@@@ of maps T: @@@@ → @@@@, known as instructions. Each instruction I has an input region IR(I), an output region OR(I), and affected regions AR(M′, I), for M′ ⊆ IR(I). For example, let I be the instruction (CLA Y) on the IBM 7094. If L is the location counter and AC is the accumulator, then IR(I) = Y ∪ L and OR(I) = AC ∪ L; if M′ is the address portion of Y, then AR(M′, I) is the address portion of AC. The fundamental properties of all these notions are derived, and computers are related to other models, such as sequential machines. The existence problem (how arbitrarily the input, output and affected regions of an instruction can be specified) is fully settled for countable memory M.