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Complete Problems for Multi-Pseudodeterministic Computations

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

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ITCS.2021.66

Author Details

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

Funding

Supported in part by NSF grants 1934884, 1849053, 1849048.

Acknowledgements

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

References

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