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Krohn-Rhodes complexity pseudovarieties are not finitely based

Published online by Cambridge University Press:  15 March 2005

John Rhodes  and
Benjamin Steinberg
John Rhodes
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA; rhodes@math.berkeley.edu
Benjamin Steinberg
Affiliation:
School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada; bsteinbg@math.carleton.ca
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Abstract

We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n>0. More specifically, for each pair of positive integers n,k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n.

Keywords

Complexityfinite basis problemthe presentation lemma
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 279 - 296
Copyright
© EDP Sciences, 2005

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