On the possibilities and limitations of pseudodeterministic algorithms

Oded Goldreich, Shafi Goldwasser, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the possibilities and limitations of pseudodeterministic algorithms, algorithms, a notion put forward by Gat and Goldwasser (2011). These are probabilistic algorithms that solve search problems such that on each input, with high probability, they output the same solution, which may be thought of as a canonical solution. We consider both the standard setting of (probabilistic) polynomial-time algorithms and the setting of (probabilistic) sublinear-time algorithms. Some of our results are outlined next. In the standard setting, we show that pseudodeterministic algorithms are more powerful than deterministic algorithms if and only if P ≠ BPP, but are weaker than general probabilistic algorithms. In the sublinear-time setting, we show that if a search problem has a pseudodeterministic algorithm of query complexity q, then this problem can be solved deterministically making O(q4) queries. This refers to total search problems. In contrast, for several natural promise search problems, we present pseudodeterministic algorithms that are much more efficient than their deterministic counterparts.

Original languageEnglish
Title of host publicationITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science
Pages127-137
Number of pages11
DOIs
StatePublished - 2013
Event2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013 - Berkeley, CA, United States
Duration: 9 Jan 201312 Jan 2013

Publication series

NameITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science

Conference

Conference2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013
Country/TerritoryUnited States
CityBerkeley, CA
Period9/01/1312/01/13

Keywords

  • bpp
  • search problems
  • sublinear-time computations
  • unique solutions
  • zpp

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