δ-Approximable Functions

  • Charles Meyssonnier
  • Paolo Boldi
  • Sebastiano Vigna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2064)


In this paper we study several notions of approximability of functions in the framework of the BSS model. Denoting with ϕ M δ the function computed by a BSS machine M when its comparisons are against −δ rather than 0, we study classes of functions f for which ϕ M δ f in some sense (pointwise, uniformly, etc.). The main equivalence results show that this notion coincides with Type 2 computability when the convergence speed is recursively bounded. Finally, we study the possibility of extending these results to computations over Archimedean fields.


Strict Inequality Recursive Function Computable Function Approximable Function Partial Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Charles Meyssonnier
    • 1
  • Paolo Boldi
    • 2
  • Sebastiano Vigna
    • 2
  1. 1.École Normale Supérieure de LyonFrance
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoItaly

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