Recursive characterization of computable real-valued functions and relations
نویسندگان
چکیده
منابع مشابه
Inferability of Recursive Real-Valued Functions
This paper presents a method of inductive inference of real-valued functions from given pairs of observed data of (x; h(x)), where h is a target function to be inferred. Each of such observed data inevitably involves some ranges of errors, and hence it is usually represented by a pair of rational numbers which show the approximate value and the error bound, respectively. On the other hand, a re...
متن کاملCharacterization of the Computable Real Numbers by Means of Primitive Recursive Functions
One usually defines the notion of a computable real number by using recursive functions. However, there is a simple way due to A. Mostowski to characterize the computable real numbers by using only primitive recursive functions. We prove Mostowski’s result differently and apply it to get other simple characterizations of this kind. For instance, a real number is shown to be computable if and on...
متن کاملOn the Inductive Inference of Recursive Real-Valued Functions
We combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functi...
متن کاملReal Recursive Functions and Real Extensions of Recursive Functions
Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...
متن کاملElementarily computable functions over the real numbers and R-sub-recursive functions
We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: we prove that they correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema. We generalize this result to all higher levels of the G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1996
ISSN: 0304-3975
DOI: 10.1016/0304-3975(95)00249-9