Two-prover one-round proof systems: Their power and their problems

Uriel Feige, L. Lovász

Research output: Chapter in Book/Report/Conference proceedingConference contribution

137 Citations (Scopus)

Abstract

We characterize the power of two-prover one-round (MIP(2,1)) proof systems, showing that MIP(2,1) = NEXPTIME. However, the following intriguing question remains open: Does parallel repetition decrease the error probability of MIP(2,1) proof systems? We use techniques based on quadratic programming to study this problem, and prove the parallel repetition conjecture in some special cases. Interestingly, our work leads to a general polynomial time heuristic for any NP-problem. We prove the effectiveness of this heuristic for several problems, such as computing the chromatic number of perfect graphs.

Original languageEnglish
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
Editors Anon
PublisherPubl by ACM
Pages733-744
Number of pages12
ISBN (Print)0897915119
Publication statusPublished - 1992
EventProceedings of the 24th Annual ACM Symposium on the Theory of Computing - Victoria, BC, Can
Duration: May 4 1992May 6 1992

Other

OtherProceedings of the 24th Annual ACM Symposium on the Theory of Computing
CityVictoria, BC, Can
Period5/4/925/6/92

Fingerprint

Quadratic programming
Polynomials
Error probability

ASJC Scopus subject areas

  • Software

Cite this

Feige, U., & Lovász, L. (1992). Two-prover one-round proof systems: Their power and their problems. In Anon (Ed.), Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 733-744). Publ by ACM.

Two-prover one-round proof systems : Their power and their problems. / Feige, Uriel; Lovász, L.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ed. / Anon. Publ by ACM, 1992. p. 733-744.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Feige, U & Lovász, L 1992, Two-prover one-round proof systems: Their power and their problems. in Anon (ed.), Conference Proceedings of the Annual ACM Symposium on Theory of Computing. Publ by ACM, pp. 733-744, Proceedings of the 24th Annual ACM Symposium on the Theory of Computing, Victoria, BC, Can, 5/4/92.
Feige U, Lovász L. Two-prover one-round proof systems: Their power and their problems. In Anon, editor, Conference Proceedings of the Annual ACM Symposium on Theory of Computing. Publ by ACM. 1992. p. 733-744
Feige, Uriel ; Lovász, L. / Two-prover one-round proof systems : Their power and their problems. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. editor / Anon. Publ by ACM, 1992. pp. 733-744
@inproceedings{1199e9fb92984f22afd386c82f3f6c0b,
title = "Two-prover one-round proof systems: Their power and their problems",
abstract = "We characterize the power of two-prover one-round (MIP(2,1)) proof systems, showing that MIP(2,1) = NEXPTIME. However, the following intriguing question remains open: Does parallel repetition decrease the error probability of MIP(2,1) proof systems? We use techniques based on quadratic programming to study this problem, and prove the parallel repetition conjecture in some special cases. Interestingly, our work leads to a general polynomial time heuristic for any NP-problem. We prove the effectiveness of this heuristic for several problems, such as computing the chromatic number of perfect graphs.",
author = "Uriel Feige and L. Lov{\'a}sz",
year = "1992",
language = "English",
isbn = "0897915119",
pages = "733--744",
editor = "Anon",
booktitle = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Publ by ACM",

}

TY - GEN

T1 - Two-prover one-round proof systems

T2 - Their power and their problems

AU - Feige, Uriel

AU - Lovász, L.

PY - 1992

Y1 - 1992

N2 - We characterize the power of two-prover one-round (MIP(2,1)) proof systems, showing that MIP(2,1) = NEXPTIME. However, the following intriguing question remains open: Does parallel repetition decrease the error probability of MIP(2,1) proof systems? We use techniques based on quadratic programming to study this problem, and prove the parallel repetition conjecture in some special cases. Interestingly, our work leads to a general polynomial time heuristic for any NP-problem. We prove the effectiveness of this heuristic for several problems, such as computing the chromatic number of perfect graphs.

AB - We characterize the power of two-prover one-round (MIP(2,1)) proof systems, showing that MIP(2,1) = NEXPTIME. However, the following intriguing question remains open: Does parallel repetition decrease the error probability of MIP(2,1) proof systems? We use techniques based on quadratic programming to study this problem, and prove the parallel repetition conjecture in some special cases. Interestingly, our work leads to a general polynomial time heuristic for any NP-problem. We prove the effectiveness of this heuristic for several problems, such as computing the chromatic number of perfect graphs.

UR - http://www.scopus.com/inward/record.url?scp=0026991175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026991175&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026991175

SN - 0897915119

SP - 733

EP - 744

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

A2 - Anon, null

PB - Publ by ACM

ER -