Structural complexity of AvgBPP

Dmitry Itsykson

doi:10.1007/978-3-642-03351-3_16

Structural complexity of AvgBPP

Dmitry Itsykson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

We study the class AvgBPP that consists of distributional problems which can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP under polynomial-time samplable distributions. Since we use deterministic reductions, the existence of a deterministic algorithm with average polynomial running time for our problem would imply AvgP = AvgBPP. Note that, while it is easy to construct a promise problem that is complete for [Mil01], it is unknown whether BPP contains complete languages. We also prove a time hierarchy theorem for AvgBPP (there are no known time hierarchy theorems for BPP). We compare average-case classes with their classical (worst-case) counterparts and show that the inclusions are proper.

Original language	English
Title of host publication	Computer Science - Theory and Applications - 4th International Computer Science Symposium in Russia, CSR 2009, Proceedings
Pages	155-166
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-03351-3_16
State	Published - 29 Oct 2009
Externally published	Yes
Event	4th International Computer Science Symposium in Russia, CSR 2009 - Novosibirsk, Russian Federation Duration: 18 Aug 2009 → 23 Aug 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5675 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Computer Science Symposium in Russia, CSR 2009
Country/Territory	Russian Federation
City	Novosibirsk
Period	18/08/09 → 23/08/09

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-03351-3_16

Cite this

Itsykson, D. (2009). Structural complexity of AvgBPP. In Computer Science - Theory and Applications - 4th International Computer Science Symposium in Russia, CSR 2009, Proceedings (pp. 155-166). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5675 LNCS). https://doi.org/10.1007/978-3-642-03351-3_16

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title = "Structural complexity of AvgBPP",

abstract = "We study the class AvgBPP that consists of distributional problems which can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP under polynomial-time samplable distributions. Since we use deterministic reductions, the existence of a deterministic algorithm with average polynomial running time for our problem would imply AvgP = AvgBPP. Note that, while it is easy to construct a promise problem that is complete for [Mil01], it is unknown whether BPP contains complete languages. We also prove a time hierarchy theorem for AvgBPP (there are no known time hierarchy theorems for BPP). We compare average-case classes with their classical (worst-case) counterparts and show that the inclusions are proper.",

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Itsykson, D 2009, Structural complexity of AvgBPP. in Computer Science - Theory and Applications - 4th International Computer Science Symposium in Russia, CSR 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5675 LNCS, pp. 155-166, 4th International Computer Science Symposium in Russia, CSR 2009, Novosibirsk, Russian Federation, 18/08/09. https://doi.org/10.1007/978-3-642-03351-3_16

Structural complexity of AvgBPP. / Itsykson, Dmitry.
Computer Science - Theory and Applications - 4th International Computer Science Symposium in Russia, CSR 2009, Proceedings. 2009. p. 155-166 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5675 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Structural complexity of AvgBPP

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