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

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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.",

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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.

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

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