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)


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


Analog Computation Recursive Function Computable Function Limit Taking Established Framework 
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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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