Abstract families of processors*

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A processor is a nondeterministic Turing-like automaton with auxiliary storage. An abstract family of processors (AFP) consists of all processors that use the storage in the same way. For a family of operations to be the output functions of an AFP, it is necessary and sufficient that it include all homomorphisms and their inverses and be closed under functional union, composition, iteration and cartesian product; necessary and sufficient that its domains (ranges) form a full AFL closed under ∩ and iterated homomorphism and that its argument-value relations be all those representable by sets of this AFL. For a family of word-sets to be the accepted languages of an AFP, it is necessary and sufficient that it be a full AFL closed under ∩ and iterated homomorphism.

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Research sponsored in part by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, USAF, under contract F1962867C0008, by the Air Force Office of Scientific Research, Office of Aerospace Research, USAF, under AFOSR Grant No. AFAFOSR-1203-67, and by NASA contract NGR 30-027-001.