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Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes, Benjamin Steinberg (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 .

Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes, Benjamin Steinberg (2010)

RAIRO - Theoretical Informatics and Applications

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.

Monoides parcialmente aditivos en la teoría de la información.

A. Bahamonde Rionda, J. S. López García (1985)

Stochastica

Partially-additive monoids (pams) were introduced by Arbib and Manes ([1]) in order to provide an algebraic approach to the semantic of recursion in theoretical computer science. Here we extend the range of application of pams for capturing information theory concepts as componibility and sequential continuity, which arise naturally in this framework.

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