Infinite-vertex free profinite semigroupoids and symbolic dynamics

@article{Almeida2009InfinitevertexFP,
  title={Infinite-vertex free profinite semigroupoids and symbolic dynamics},
  author={Jorge Almeida and Alfredo Costa},
  journal={Journal of Pure and Applied Algebra},
  year={2009},
  volume={213},
  pages={605-631}
}

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References

SHOWING 1-10 OF 53 REFERENCES
SYMBOLIC DYNAMICS IN FREE PROFINITE SEMIGROUPS
This is a survey and announcement of recent results on the structure of free profinite semigroups using techniques and results from symbolic dynamics. The intimate connection between uniformly
Subword Complexity of Profinite Words and Subgroups of Free Profinite Semigroups
TLDR
A general scheme to produce free profinite subgroups of freeProfinite semigroups of the same rank using iterated continuous endomorphisms, subword complexity, and the associated entropy and a proof that the complement of the minimal ideal in a free Profinite semigroup on more than one generator is closed.
Profinite semigroups and applications
Profinite semigroups may be described briefly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a
Finite Semigroups and Universal Algebra
Part 1 Finite universal algebra: elements of universal algebra order and topology finite algebras decidability. Part 2 Finite semigroups and monoids: permutativity operators relating semigroups and
Profinite Semigroups, Varieties, Expansions and the Structure of Relatively Free Profinite Semigroups
TLDR
The structure of the minimal ideal of relatively free profinite semigroups is studied showing, in particular, that the minimal Ideal of the free Profinite semigroup on a finite set with more than two generators is not a relatively freeProfinite completely simple semigroup, as well as some generalizations to related pseudovarieties.
Profinite Methods in Semigroup Theory
  • P. Weil
  • Mathematics
    Int. J. Algebra Comput.
  • 2002
TLDR
The contribution of profinite methods and the way they enriched and modified finite semigroup theory are surveyed.
Locally testable semigroups
The locally testable semigroups were discovered in the study of finite automata (see [8], [12] for history and motivation). In this paper, we study the locally testable semigroups from a purely
Conjugacy Invariants of Subshifts: an Approach from Profinite Semigroup Theory
  • A. Costa
  • Mathematics
    Int. J. Algebra Comput.
  • 2006
TLDR
A shift equivalence invariant is obtained, improving an invariant introduced by Beal, Fiorenzi and Perrin using different techniques, and used to prove that some almost finite type subshifts with the same zeta function are not shift equivalent.
The pseudoidentity problem and reducibility for completely regular semigroups
Dedicated to George Szekeres on the occasion of his 90th birthday Necessary and sufficient conditions for equality over the pseudovariety CR of all finite completely regular semigroups are obtained.
Algebraic theory of machines, languages and semigroups
Abstract : The book is an integrated exposition of the algebraic, and especially semigroup-theoretic, approach to machines and languages. It is designed to carry the reader from the elementary theory
...
...