Macrotransducers, Continuity and Computability
by
Leonid P. Lisovik
Department of Cybernetics, Kiev National University, Kiev, 01017,

Every continuous real function can be presented by R-transducer. Correspondingly it can be presented by computation tree which is infinite labelled tree. Thence macrotransducers over infinite labelled trees can be used to present continuous operators in the functional spaces, for instance, in space C[0, 1]. Relations between computability, realizability (by means of macrotransducers) and continuity are under consideration in this paper as well as question about algebraic characterization of computable real functions. We give here one theorem which assertaines that continuity implies computability when very easy additional requirements are imposed. Simple proofs for KLS-theorem and Ceitin's Theorem are given. There are many interesting examoles of continuous functions defined by finite R-transducers.

Date received: March 17, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cajy-17.