On primitive recursive algorithms and the greatest common divisor function

Authors:
Yiannis N. Moschovakis
Affiliations:
Department of Mathematics, University of California, 405 Hilgard Avenue, Los Angeles, CA and Department of Mathematics, University of Athens, Athens, Greece
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We establish linear lower bounds for the complexity of non-trivial, primitive recursive algorithms from piecewise linear given functions. The main corollary is that logtime algorithms for the greatest common divisor from such givens (such as Stein's) cannot be matched in efficiency by primitive recursive algorithms from the same given functions. The question is left open for the Euclidean algorithm, which assumes the remainder function.