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On Higher-Order Probabilistic Subrecursion

  • Flavien Breuvart
  • Ugo Dal LagoEmail author
  • Agathe Herrou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)

Abstract

We study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like Gödel’s \(\mathbb {T}\) with various forms of probabilistic choice operators may result in calculi which are not equivalent as for the class of distributions they give rise to, although they all guarantee almost-sure termination. Along the way, we introduce a probabilistic variation of the classic reducibility technique, and we prove that the simplest form of probabilistic choice leaves the expressive power of \(\mathbb {T}\) essentially unaltered. The paper ends with some observations about functional expressivity: expectedly, all the considered calculi represent precisely the functions which \(\mathbb {T}\) itself represents.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Flavien Breuvart
    • 1
  • Ugo Dal Lago
    • 1
    • 2
    Email author
  • Agathe Herrou
    • 3
  1. 1.INRIASophia AntipolisFrance
  2. 2.University of BolognaBolognaItaly
  3. 3.ENS de LyonLyonFrance

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