A Recursion-Theoretic Characterization of the Probabilistic Class PP

Authors Ugo Dal Lago, Reinhard Kahle, Isabel Oitavem

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Author Details

Ugo Dal Lago
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France
Reinhard Kahle
  • Carl Friedrich von Weizsäcker Center, Universität Tübingen, Germany
  • Center for Mathematics and Applications (CMA), FCT, Nova University Lisbon, Caparica, Portugal
Isabel Oitavem
  • Center for Mathematics and Applications (CMA), FCT, Nova University Lisbon, Caparica, Portugal
  • Department of Mathematics, FCT, Nova University Lisbon, Caparica, Portugal

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Ugo Dal Lago, Reinhard Kahle, and Isabel Oitavem. A Recursion-Theoretic Characterization of the Probabilistic Class PP. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 35:1-35:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Probabilistic complexity classes, despite capturing the notion of feasibility, have escaped any treatment by the tools of so-called implicit-complexity. Their inherently semantic nature is of course a barrier to the characterization of classes like BPP or ZPP, but not all classes are semantic. In this paper, we introduce a recursion-theoretic characterization of the probabilistic class PP, using recursion schemata with pointers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Recursive functions
  • Implicit complexity
  • tree-recursion
  • probabilistic classes
  • polynomial time
  • PP


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