Macrotransducers and Applicative Systems for Partially Continuous Functions

Authors:
L. P. Lisovik
Affiliations:
Taras Shevchenko University, Kiev, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2001

Citing 2
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Abstract

The \Delta-calculus is an applicative system having the axioms of universality and approximation and the so-called is-m-n-axiom. It is proved that this calculus is interpreted in the theory of partially continuous operators on the space iC[0, 1] consisting of continuous real functions defined on the segment [0, 1] . The problems of realizability, continuity, and computability are considered. The realizability of functionals and operators is understood to be the possibility of their representation by macrotransducers over labeled trees.