The efficiency of primitive recursive functions: A programmer's view
نویسنده
چکیده
منابع مشابه
Equivalence of BSS scalar - and vector - recursion
BSS-computable functions can be approached in two ways: from the point of view of computations performed by machines or under the angle of the theory of recursive functions. The goal of this paper is to answer negatively a basic question of the theory of BSS-recursive functions, namely " is vector-recursion stronger than scalar recursion? "
متن کاملPrimitive recursive functions versus partial recursive functions: comparing the degree of undecidability
Consider a decision problem whose instance is a function. Its degree of undecidability, measured by the corresponding class of the arithmetic (or Kleene-Mostowski) hierarchy hierarchy, may depend on whether the instance is a partial recursive or a primitive recursive function. A similar situation happens for results like Rice Theorem (which is false for primitive recursive functions). Classical...
متن کاملTHE a - UNION THEOREM AND GENERALIZED PRIMITIVE RECURSION
A generalization to a-recursion theory of the McCreight-Meyer Union Theorem is proved. Theorem. Let <5> be an a-computational complexity measure and {ft\e < a) an a-r.e. strictly increasing sequence of a-recursive functions. Then there exists an a-recursive function k such that C* ~ U «<aC/f • The proof entails a no-injury cancellation atop a finite-injury priority construction and necessitates...
متن کاملUnary Primitive Recursive Functions
In this article, we will study certain reductions in the schemes that conform unary primitive recursive functions (i.e. primitive recursive functions of one argument) and we will extend some results previously researched by R. M. Robinson in [15]. Furthermore, we will introduce formal notation for unary primitive recursive functions. §
متن کاملOn primitive recursive algorithms and the greatest common divisor function
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 algor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 594 شماره
صفحات -
تاریخ انتشار 2015