Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes; Benjamin Steinberg

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

  • Volume: 39, Issue: 1, page 279-296
  • ISSN: 0988-3754

Abstract

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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 .

How to cite

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Rhodes, John, and Steinberg, Benjamin. "Krohn-Rhodes complexity pseudovarieties are not finitely based." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 279-296. <http://eudml.org/doc/245322>.

@article{Rhodes2005,
abstract = {We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most $n$ is not finitely based for all $n&gt;0$. 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 $n$.},
author = {Rhodes, John, Steinberg, Benjamin},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {complexity; finite basis problem; the presentation lemma; pseudovarieties of finite monoids; pseudoidentity bases; wreath products; Krohn-Rhodes complexity},
language = {eng},
number = {1},
pages = {279-296},
publisher = {EDP-Sciences},
title = {Krohn-Rhodes complexity pseudovarieties are not finitely based},
url = {http://eudml.org/doc/245322},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Rhodes, John
AU - Steinberg, Benjamin
TI - Krohn-Rhodes complexity pseudovarieties are not finitely based
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 279
EP - 296
AB - We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most $n$ is not finitely based for all $n&gt;0$. 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 $n$.
LA - eng
KW - complexity; finite basis problem; the presentation lemma; pseudovarieties of finite monoids; pseudoidentity bases; wreath products; Krohn-Rhodes complexity
UR - http://eudml.org/doc/245322
ER -

References

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