Generating the Greatest Common Divisor, and Limitations of Primitive Recursive Algorithms
Tóm tắt
The greatest common divisor of two integers cannot be
generated in a uniformly bounded number of steps from those integers
using arithmetic operations. The proof uses an elementary model-theoretic
construction that enables us to focus on
“integers with transcendental ratio.”
This unboundedness result is part of the solution of a problem posed
by Y. Moschovakis on limitations of primitive recursive
algorithms for computing the greatest common divisor function.
Tài liệu tham khảo
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L. Colson (1991) ArticleTitleAbout primitive recursive algorithms Theoret. Comput. Sci. 83 57–69 Occurrence Handle0744.03042
L. van den Dries and A.J. Wilkie, The laws of integer divisibility, and solution sets of linear divisibility conditions, J. Symbolic Logic (to appear)
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