| Issue |
RAIRO-Theor. Inf. Appl.
Volume 39, Number 1, January-March 2005
Imre Simon, the tropical computer scientist
|
|
|---|---|---|
| Page(s) | 279 - 296 | |
| DOI | https://doi.org/10.1051/ita:2005016 | |
| Published online | 15 March 2005 | |
Krohn-Rhodes complexity pseudovarieties are not finitely based
1
Department of Mathematics,
University of California at Berkeley, Berkeley, CA 94720, USA;
rhodes@math.berkeley.edu
2
School of Mathematics and
Statistics, Carleton University, 1125 Colonel By Drive, Ottawa,
Ontario K1S 5B6, Canada; bsteinbg@math.carleton.ca
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.
Mathematics Subject Classification: 20M07
Key words: Complexity / finite basis problem / the presentation lemma
© EDP Sciences, 2005
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