Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus

Alexander Razborov; Avi Wigderson; Andrew Yao

doi:10.1145/258533.258673

Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus

Alexander Razborov^*
, Avi Wigderson
, Andrew Yao

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

28 Scopus citations

Abstract

Read once branching programs are investigated for the following search problem: given a Boolean m×n matrix with m>n, find either an all-zero row, or two 1's in some column. Exponential lower bounds are proven if the model is restricted by requiring the branching program either to finish one row of queries before asking queries about another row or put the dual column restriction. A special class of resolution proofs is investigated for P H P_n^m that operate with positive clauses of rectangular shape and termed it rectangular calculus. The rectangular calculus is shown to be equivalent to the column model on one hand, and to the transversal calculus on the other hand.

Original language	English
Pages (from-to)	739-748
Number of pages	10
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/258533.258673
State	Published - 1997
Externally published	Yes
Event	Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA Duration: 4 May 1997 → 6 May 1997

Access to Document

10.1145/258533.258673

Cite this

@article{0a4943bf84d2402fb2960d439fea12dc,

title = "Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus",

abstract = "Read once branching programs are investigated for the following search problem: given a Boolean m×n matrix with m>n, find either an all-zero row, or two 1's in some column. Exponential lower bounds are proven if the model is restricted by requiring the branching program either to finish one row of queries before asking queries about another row or put the dual column restriction. A special class of resolution proofs is investigated for P H Pnm that operate with positive clauses of rectangular shape and termed it rectangular calculus. The rectangular calculus is shown to be equivalent to the column model on one hand, and to the transversal calculus on the other hand.",

author = "Alexander Razborov and Avi Wigderson and Andrew Yao",

year = "1997",

doi = "10.1145/258533.258673",

language = "אנגלית",

pages = "739--748",

journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

issn = "0734-9025",

publisher = "Association for Computing Machinery",

note = "Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing ; Conference date: 04-05-1997 Through 06-05-1997",

}

TY - JOUR

T1 - Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus

AU - Razborov, Alexander

AU - Wigderson, Avi

AU - Yao, Andrew

PY - 1997

Y1 - 1997

N2 - Read once branching programs are investigated for the following search problem: given a Boolean m×n matrix with m>n, find either an all-zero row, or two 1's in some column. Exponential lower bounds are proven if the model is restricted by requiring the branching program either to finish one row of queries before asking queries about another row or put the dual column restriction. A special class of resolution proofs is investigated for P H Pnm that operate with positive clauses of rectangular shape and termed it rectangular calculus. The rectangular calculus is shown to be equivalent to the column model on one hand, and to the transversal calculus on the other hand.

AB - Read once branching programs are investigated for the following search problem: given a Boolean m×n matrix with m>n, find either an all-zero row, or two 1's in some column. Exponential lower bounds are proven if the model is restricted by requiring the branching program either to finish one row of queries before asking queries about another row or put the dual column restriction. A special class of resolution proofs is investigated for P H Pnm that operate with positive clauses of rectangular shape and termed it rectangular calculus. The rectangular calculus is shown to be equivalent to the column model on one hand, and to the transversal calculus on the other hand.

UR - https://www.scopus.com/pages/publications/0030642913

U2 - 10.1145/258533.258673

DO - 10.1145/258533.258673

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.conferencearticle???

AN - SCOPUS:0030642913

SN - 0734-9025

SP - 739

EP - 748

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

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

T2 - Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing

Y2 - 4 May 1997 through 6 May 1997

ER -

Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus

Abstract

Access to Document

Other files and links

Fingerprint

Cite this