research-article

The size of generating sets of powers

Author:

Dmitriy ZhukAuthors Info & Claims

Volume 167, Issue C

Pages 91 - 103

https://doi.org/10.1016/j.jcta.2019.04.003

Published: 01 October 2019 Publication History

Abstract

For a finite algebra ( A ; F ), i.e. a set F of operations on a finite set A, we study the minimal size of a generating set of A n, which is called the growth rate of the algebra. We prove that a growth rate is either bounded by a polynomial in n, or exponential in n, and explain how to find a generating set of polynomial size if it exists. For idempotent algebras we give a simple criterion for an algebra to have an exponential growth rate.

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Cited By

Zhuk DMartin B(2022)QCSP Monsters and the Demise of the Chen ConjectureJournal of the ACM10.1145/356382069:5(1-44)Online publication date: 15-Sep-2022
https://dl.acm.org/doi/10.1145/3563820
Carvalho CMadelaine FMartin BZhuk D(undefined)The complexity of quantified constraints: collapsibility, switchability and the algebraic formulationACM Transactions on Computational Logic10.1145/3568397
https://dl.acm.org/doi/10.1145/3568397

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The size of generating sets of powers

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cover image Journal of Combinatorial Theory Series A

Journal of Combinatorial Theory Series A Volume 167, Issue C

Oct 2019

564 pages

ISSN:0097-3165

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Elsevier Inc.

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Academic Press, Inc.

United States

Publication History

Published: 01 October 2019

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Cited By

Zhuk DMartin B(2022)QCSP Monsters and the Demise of the Chen ConjectureJournal of the ACM10.1145/356382069:5(1-44)Online publication date: 15-Sep-2022
https://dl.acm.org/doi/10.1145/3563820
Carvalho CMadelaine FMartin BZhuk D(undefined)The complexity of quantified constraints: collapsibility, switchability and the algebraic formulationACM Transactions on Computational Logic10.1145/3568397
https://dl.acm.org/doi/10.1145/3568397

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