Computability properties of the Gau ian function
نویسندگان
چکیده
We speculate on the Gau ian function [x] as an example of a noncontinuous function which is nevertheless possessed of some properties of computability. An algorithm how to compute [x] for a single computable real number is rst described, followed by a remark that [x] does not necessarily preserve sequential computability. Second, [x] is studied in the light of the notion of upper semi-computability. Then two Fr echet spaces, R Z and L 1 loc (R) , in which the Gau ian function is computable, will be taken up.
منابع مشابه
On the Computability of Region-Based Euclidean Logics
By a Euclidean logic, we understand a formal language whose variables range over subsets of Euclidean space, of some fixed dimension, and whose non-logical primitives have fixed meanings as geometrical properties, relations and operations involving those sets. In this paper, we consider first-order Euclidean logics with primitives for the properties of connectedness and convexity, the binary re...
متن کاملCharacteristic Properties of Majorant-Computability over the Reals
Characteristic properties of majorant-computable real-valued functions are studied. A formal theory of computability over the reals which satisses the requirements of numerical analysis used in Computer Science is constructed on the base of the deenition of majorant-computa-bility proposed in 13]. A model-theoretical characterization of majorant-computability real-valued functions and their dom...
متن کاملA Mechanisation of Computability Theory in HOL
This paper describes a mechanisation of computability theory in HOL using the Unlimited Register Machine (URM) model of computation. The URM model is rst speciied as a rudimentary machine language and then the notion of a computable function is derived. This is followed by an illustration of the proof of a number of basic results of computability which include various closure properties of comp...
متن کاملComputability on the Probability Measures on the Borel Sets of the Unit Interval
Scientists apply digital computers to perform computations on natural numbers, nite strings, real numbers and more general objects like sets, functions and measures. While computability theory on many countable sets is well established and for computability on the real numbers several (unfortunately mutually non-equivalent) deenitions are being studied, in particular for measures no computabili...
متن کاملA Note on Rademacher Functions and Computability
We will speculate on some computational properties of the system of Rademacher functions f n g. The n-th Rademacher function n is a step function on the interval [0; 1), jumping at nitely many dyadic rationals of size 1 2 n and assuming values f1; 1g alternatingly.
متن کامل