Complete Problems for Multi-Pseudodeterministic Computations
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.
Pseudodeterminism
Completeness
Collision Probability
Circuit Acceptance
Entropy Approximation
Theory of computation~Probabilistic computation
Theory of computation~Problems, reductions and completeness
66:1-66:16
Regular Paper
Supported in part by NSF grants 1934884, 1849053, 1849048.
We thank Oded Goldrecih for comments and suggestions on an earlier draft of this paper. We also thank anonymous reviewers for helpful comments.
Peter
Dixon
Peter Dixon
Department of Computer Science, Iowa State University, Ames, IA, USA
A.
Pavan
A. Pavan
Department of Computer Science, Iowa State University, Ames, IA, USA
N. V.
Vinodchandran
N. V. Vinodchandran
Department of Computer Science and Engineering, University of Nebraska, Lincoln, NE, USA
10.4230/LIPIcs.ITCS.2021.66
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Peter Dixon, A. Pavan, and N. V. Vinodchandran
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