## Instruction Set Completeness Theorem: Concept, Relevance, Proof, and Example for Processor Architecture

**Authors:** William F. Gilreath

The Instruction Set Completeness Theorem is first formally defined and discussed in the seminal work on one-instruction set computing—the book Computer Architecture: A Minimalist Perspective.
Yet the original formalism of the Instruction Set Completeness Theorem did not provide a definitive, explicit mathematical proof of completeness, analyze both singular and plural instruction sets that were either complete or incomplete, nor examine the significance of the theorem to computer architecture instruction sets.
A mathematical proof of correctness shows the equivalence of the Instruction Set Completeness Theorem to a Turing machine, a hypothetical model of computation, and thereby establishes the mathematical truth of the Instruction Set Completeness Theorem. With a more detailed examination of the Instruction Set Completeness Theorem develops several surprising conclusions for both the instruction set completeness theorem, and the instruction sets for a computer architecture.

**Comments:** 22 Pages. Published in the General Science Journal

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### Submission history

[v1] 2019-10-27 07:25:40

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