The New Promise of Analog Computation

Authors:
José Félix Costa;Bruno Loff;Jerzy Mycka
Affiliations:
Department of Mathematics, Instituto Superior Técnico Universidade Técnica de Lisboa, Lisboa, Portugal and Centro de Matemática e Aplicações Fundamentais do Complexo Inter ...;Centro de Matemática e Aplicações Fundamentais do Complexo Interdisciplinar, Universidade de Lisboa, Lisbon, Portugal;Institute of Mathematics, University of Maria Curie-Skłodowska, Lublin, Poland
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

Citing 10
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Abstract

We show that, using our more or less established framework of inductive definition of real-valued functions(work started by Cristopher Moore in [9]) together with ideas and concepts of standard computability we can prove theorems of Analysis. Then we will consider our ideas as a bridging tool between the standard Theory of Computability (and Complexity)on one side and Mathematical Analysison the other, making real recursive functions a possible branch of Descriptive Set Theory. What follows is an Extended Abstract directed to a large audience of CiE 2007, Special Session on Logic and New Paradigms of Computability. (Proofs of statements can be found in a detailed long paper at the address http://fgc.math.ist.utl.pt/papers/hierarchy.pdf.)