On (valiant’s) polynomial-size monotone formula for majority

Oded Goldreich

doi:https://doi.org/10.1007/978-3-030-43662-9_3

On (valiant’s) polynomial-size monotone formula for majority

Oded Goldreich

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This exposition provides a proof of the existence of polynomial-size monotone formula for Majority. The exposition follows the main principles of Valiant’s proof (J. Algorithms, 1984), but deviates from it in the actual implementation. Specifically, we show that, with high probability, a full ternary tree of depth 2.71log₂n computes the majority of n values when each leaf of the tree is assigned at random one of the n values.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher	Springer Verlag
Chapter	3
Pages	17-23
Number of pages	7
DOIs	https://doi.org/10.1007/978-3-030-43662-9_3
State	Published - 4 Apr 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12050 LNCS

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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https://doi.org/10.1007/978-3-030-43662-9_3

Cite this

Goldreich, O. (2020). On (valiant’s) polynomial-size monotone formula for majority. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 17-23). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-43662-9_3

Goldreich, Oded. / On (valiant’s) polynomial-size monotone formula for majority. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag, 2020. pp. 17-23 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Goldreich, O 2020, On (valiant’s) polynomial-size monotone formula for majority. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12050 LNCS, Springer Verlag, pp. 17-23. https://doi.org/10.1007/978-3-030-43662-9_3

On (valiant’s) polynomial-size monotone formula for majority. / Goldreich, Oded.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag, 2020. p. 17-23 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12050 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Goldreich O. On (valiant’s) polynomial-size monotone formula for majority. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2020. p. 17-23. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-030-43662-9_3

On (valiant’s) polynomial-size monotone formula for majority

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