TY - GEN

T1 - On the possibilities and limitations of pseudodeterministic algorithms

AU - Goldreich, Oded

AU - Goldwasser, Shafi

AU - Ron, Dana

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - bpp

KW - search problems

KW - sublinear-time computations

KW - unique solutions

KW - zpp

UR - http://www.scopus.com/inward/record.url?scp=84873365512&partnerID=8YFLogxK

U2 - 10.1145/2422436.2422453

DO - 10.1145/2422436.2422453

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84873365512

SN - 9781450318594

T3 - ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science

SP - 127

EP - 137

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

Y2 - 9 January 2013 through 12 January 2013

ER -