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The notion of pseudovarieties of homomorphisms onto finite monoids
was recently introduced by Straubing as an algebraic characterization
for certain classes of regular languages.
In this paper we provide a mechanism of equational description
of these pseudovarieties based on an appropriate
generalization of the notion of implicit operations.
We show that the resulting metric monoids of implicit operations
coincide with the standard ones,
the only difference being the actual interpretation of pseudoidentities.
As...
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
The fixed point submonoid of an endomorphism of a free product of a free monoid and
cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s
result on the computability of the fixed point subgroup of a free group automorphism is
generalized to endomorphisms of free products of a free monoid and a free group which are
automorphisms of the maximal subgroup.
We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors.
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