منابع مشابه
Streamlined subrecursive degree theory
The study of honest elementary degrees has its roots in subrecursion theory from the nineteen seventies. Some relevant papers are Meyer & Ritchie [12] and Machtey [9–11]. These papers deal with subrecursive function classes being generated by so-called honest functions where an honest function is defined relative to a subrecursive class S and a model of computation: a function f : N → N is hone...
متن کاملAn analog characterization of the subrecursive functions
We study a restricted version of Shannon’s General Purpose Analog Computer in which we only allow the machine to solve linear differential equations. This corresponds to only allowing local feedback in the machine’s variables. We show that if this computer is allowed to sense inequalities in a differentiable way, then it can compute exactly the elementary functions. Furthermore, we show that if...
متن کاملSome subrecursive versions of Grzegorczyk's Uniformity Theorem
A theorem published by A. Grzegorczyk in 1955 states a certain kind of effective uniform continuity of computable functionals that transform systems of total functions in the set of the natural numbers and of natural numbers into natural numbers. Namely, for any such functional a computable functional with one function-argument and the same number-arguments exists such that the values of the fi...
متن کاملThe Decidable Properties of Subrecursive Functions
What can be decided or semidecided about a primitive recursive function, given a definition of that function by primitive recursion? What about subrecursive classes other than primitive recursive functions? We provide a complete and explicit characterization of the decidable and semidecidable properties. This characterization uses a variant of Kolmogorov complexity where only programs in a subr...
متن کاملOn subrecursive representability of irrational numbers
We consider various ways to represent irrational numbers by subrecursive functions: via Cauchy sequences, Dedekind cuts, trace functions, several variants of sum approximations and continued fractions. Let S be a class of subrecursive functions. The set of irrational numbers that can be obtained with functions from S depends on the representation. We compare the sets obtained by the different r...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.11.004