NDLI: Pseudorandomness for approximate counting and sampling

Content Provider	IEEE Xplore Digital Library
Author	Shaltiel, R. Umans, C.
Copyright Year	2005
Description	Author affiliation: Dept. of Comput. Sci., Haifa Univ., Israel (Shaltiel, R.)
Abstract	We study computational procedures that use both randomness and nondeterminism. Examples are Arthur-Merlin games and approximate counting and sampling of NP-witnesses. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allows one to "boost" a given hardness assumption. One special case is a proof that EXP /spl nsube/ NP/poly /spl rArr/ EXP /spl nsube/ P/sub /spl par///sup NP//poly. In words, if there is a problem in EXP that cannot be computed by poly-size nondeterministic circuits then there is one which cannot be computed by poly-size circuits that make non-adaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize Arthur-Merlin games (i.e., show AM = NP) are in fact all equivalent. In addition to simplifying the framework of AM derandomization, we show that this "unified assumption" suffices to de-randomize several other probabilistic procedures. For these results we define two new primitives that we regard as the natural pseudorandom objects associated with approximate counting and sampling of NP-witnesses. We use the "boosting" theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM. As a consequence, under this assumption, there are deterministic polynomial time algorithms that use non-adaptive NP-queries and perform the following tasks: 1) approximate counting of NP-witnesses: given a Boolean circuit A, output r such that (1 - /spl epsi/)\|A/sup -1/(1)\| /spl les/ r les; \|A/sup -1/(1)\|. 2) pseudorandom sampling of NP-witnesses: given a Boolean circuit A, produce a polynomial-size sample space that is computationally indistinguishable from the uniform distribution over A/sup -1/(1). We also present applications. For example, we observe that Cai's proof that S/sub 2//sup p/ /spl sube/ ZPP/sup NP/ and the learning algorithm of Bshouty et al. can be seen as reductions to sampling that are not probabilistic. As a consequence they can be derandomized under the assumption stated above, which is weaker than the assumption that was previously known to suffice.
Sponsorship	IEEE Comput. Soc. Tech. Comm. on Math. Found. of Comput
Starting Page	212
Ending Page	226
File Size	253170
Page Count	15
File Format	PDF
ISBN	0769523641
ISSN	10930159
DOI	10.1109/CCC.2005.26
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-06-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sampling methods Circuit testing Computer science Polynomials Scholarships Distributed computing Computational modeling Computational complexity
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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