Non-deterministic communication complexity with few witnesses

Mauricio Karchmer; Ilan Newman; Mike Saks; Avi Wigderson

doi:10.1016/S0022-0000(05)80049-2

Non-deterministic communication complexity with few witnesses

Mauricio Karchmer, Ilan Newman, Mike Saks, Avi Wigderson

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We study non-deterministic communication protocols in which no input has too many witnesses. Define n_k(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for n_k(f). Our first result shows that n_k(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds n_k(f) by log(rk(M_f))/k - 1, where rk(M_f) is the rank of the representing matrix of f. As a consequence, it follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.

Original language	English
Pages (from-to)	247-257
Number of pages	11
Journal	Journal of Computer and System Sciences
Volume	49
Issue number	2
DOIs	https://doi.org/10.1016/S0022-0000(05)80049-2
State	Published - Oct 1994

Bibliographical note

Funding Information:
In the two-party communication complexity model, two parties compute a function that depends on both of their (initially private) inputs. Roughly speaking, the deterministic communication complexity of a function f(x, y) is the minimum * Supported by NSF Grant CCR90-10533. t This work was done while the author was at the Royal Instituut of Technology, Stockholm. Supported in part by NSF Grant CCR89-11388, and AFOSR Grants 89-0512B and 90-0008.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1016/S0022-0000(05)80049-2

Cite this

@article{3ee8d7d2cd32446eaccf1423cfe258dd,

title = "Non-deterministic communication complexity with few witnesses",

abstract = "We study non-deterministic communication protocols in which no input has too many witnesses. Define nk(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for nk(f). Our first result shows that nk(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds nk(f) by log(rk(Mf))/k - 1, where rk(Mf) is the rank of the representing matrix of f. As a consequence, it follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.",

author = "Mauricio Karchmer and Ilan Newman and Mike Saks and Avi Wigderson",

note = "Funding Information: In the two-party communication complexity model, two parties compute a function that depends on both of their (initially private) inputs. Roughly speaking, the deterministic communication complexity of a function f(x, y) is the minimum * Supported by NSF Grant CCR90-10533. t This work was done while the author was at the Royal Instituut of Technology, Stockholm. Supported in part by NSF Grant CCR89-11388, and AFOSR Grants 89-0512B and 90-0008.",

year = "1994",

month = oct,

doi = "10.1016/S0022-0000(05)80049-2",

language = "English",

volume = "49",

pages = "247--257",

journal = "Journal of Computer and System Sciences",

issn = "0022-0000",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Non-deterministic communication complexity with few witnesses

AU - Karchmer, Mauricio

AU - Newman, Ilan

AU - Saks, Mike

AU - Wigderson, Avi

N1 - Funding Information: In the two-party communication complexity model, two parties compute a function that depends on both of their (initially private) inputs. Roughly speaking, the deterministic communication complexity of a function f(x, y) is the minimum * Supported by NSF Grant CCR90-10533. t This work was done while the author was at the Royal Instituut of Technology, Stockholm. Supported in part by NSF Grant CCR89-11388, and AFOSR Grants 89-0512B and 90-0008.

PY - 1994/10

Y1 - 1994/10

N2 - We study non-deterministic communication protocols in which no input has too many witnesses. Define nk(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for nk(f). Our first result shows that nk(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds nk(f) by log(rk(Mf))/k - 1, where rk(Mf) is the rank of the representing matrix of f. As a consequence, it follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.

AB - We study non-deterministic communication protocols in which no input has too many witnesses. Define nk(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for nk(f). Our first result shows that nk(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds nk(f) by log(rk(Mf))/k - 1, where rk(Mf) is the rank of the representing matrix of f. As a consequence, it follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.

UR - http://www.scopus.com/inward/record.url?scp=0028518133&partnerID=8YFLogxK

U2 - 10.1016/S0022-0000(05)80049-2

DO - 10.1016/S0022-0000(05)80049-2

M3 - Article

AN - SCOPUS:0028518133

SN - 0022-0000

VL - 49

SP - 247

EP - 257

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 2

ER -

Non-deterministic communication complexity with few witnesses

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this