The New Promise of Analog Computation

  • José Félix Costa
  • Bruno Loff
  • Jerzy Mycka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

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 Analysis on 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.)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • José Félix Costa
    • 1
    • 2
  • Bruno Loff
    • 2
  • Jerzy Mycka
    • 3
  1. 1.Department of Mathematics, Instituto Superior Técnico Universidade Técnica de Lisboa, LisboaPortugal
  2. 2.Centro de Matemática e Aplicações Fundamentais do Complexo Interdisciplinar, Universidade de Lisboa, LisbonPortugal
  3. 3.Institute of Mathematics, University of Maria Curie-Skłodowska, LublinPoland

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