Complete Problems for Multi-Pseudodeterministic Computations

Authors Peter Dixon, A. Pavan, N. V. Vinodchandran

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Peter Dixon
  • Department of Computer Science, Iowa State University, Ames, IA, USA
A. Pavan
  • Department of Computer Science, Iowa State University, Ames, IA, USA
N. V. Vinodchandran
  • Department of Computer Science and Engineering, University of Nebraska, Lincoln, NE, USA


We thank Oded Goldrecih for comments and suggestions on an earlier draft of this paper. We also thank anonymous reviewers for helpful comments.

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Peter Dixon, A. Pavan, and N. V. Vinodchandran. Complete Problems for Multi-Pseudodeterministic Computations. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 66:1-66:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We exhibit several computational problems that are complete for multi-pseudodeterministic computations in the following sense: (1) these problems admit 2-pseudodeterministic algorithms (2) if there exists a pseudodeterministic algorithm for any of these problems, then any multi-valued function that admits a k-pseudodeterministic algorithm for a constant k, also admits a pseudodeterministic algorithm. We also show that these computational problems are complete for Search-BPP: a pseudodeterministic algorithm for any of these problems implies a pseudodeterministic algorithm for all problems in Search-BPP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Problems, reductions and completeness
  • Pseudodeterminism
  • Completeness
  • Collision Probability
  • Circuit Acceptance
  • Entropy Approximation


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