NDLI: Superpolynomial Lower Bounds for Monotone Span Programs 1

Please wait, while we are loading the content...

Superpolynomial Lower Bounds for Monotone Span Programs 1

Content Provider	Semantic Scholar
Author	Wigderson, Avi
Copyright Year	1996
Abstract	In this paper we obtain the rst superpolynomial lower bounds for monotone span programs computing explicit functions. The best previous lower bound was (n5=2) by Beimel, G al, Paterson [BGP]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. We prove an n (log n= log log n) lower bound for an explicit family of monotone Boolean functions in n variables, which implies the same lower bound for the size of monotone span programs for the clique problem. Our results give the rst superpolynomial lower bounds for linear secret sharing schemes. We demonstrate the surprising power of monotone span programs by exhibiting a function computable in this model in linear size while requiring superpolynomial size monotone circuits and exponential size monotone formulae. We also show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary elds. 1Part of this work has been presented at the 28th ACM STOC'96. The second two authors wish to thank DIMACS for its hospitality and acknowledge its supporting agencies, the National Science Foundation under contract STC-91-19999 and the New Jersey Commission on Science and Technology. 2Department of Computer Science, University of Chicago, Chicago IL 60637-1504. E-mail: laci@cs.uchicago.edu. 3Institute for Advanced Study, PrincetonN.J. 08540 and DIMACS at Princeton University. Email: panni@cs.princeton.edu. { Research supported by NSF Grant DMS-9304580. 4Institute of Computer Science, Hebrew University, Jerusalem, Israel. Currently visiting the Institute for Advanced Study, Princeton,N. J. 08540 and DIMACS at PrincetonUniversity. Research supported by the Sloan Foundation, American-Israeli BSF grant 92-00106, and the Wolfson Research Awards, administered by the Israel Academy of Sciences. 1
File Format	PDF HTM / HTML
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

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