The Recognition Problem for the Set of Perfect Squares
نویسنده
چکیده
Lower bound~ on the capacity and on the product of capacity and computation time are obtained for machines which recognize the set of squares. The bound on capacity is approached to within a factor of four by a specific machine which carries out a test based on the fact that every non-square is a quadratic non-residue of some rational prime. A machine which carries out a te st based on the standard root-extraction algorithm is substantially Ie ss efficient in this respect. For neither machine is the bound on the capacity-time product closely approached.
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