Abstract
A new proof is given for the well-known theorem of Putnam, Davis, and Robinson on exponential diophantine representation of recursively enumerable sets. Starting from the usual definition of r.e. sets via Turing machines, a new method of arithmetization is given. This new method leads directly to a purely existential exponential formula. The new proof may be more suitable for a course on the theory of algorithms because it requires less knowledge of number theory.
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Translated by J. P. Jones and L. Guy.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk-SSSR, Vol. 60, pp. 75–92, 1976. Main results announced June 19, 1975.
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Matiyasevich, Y.V. A new proof of the theorem on exponential diophantine representation of enumerable sets. J Math Sci 14, 1475–1486 (1980). https://doi.org/10.1007/BF01693980
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DOI: https://doi.org/10.1007/BF01693980