A note on intersections of free submonoids of a free monoid

2006 ◽  
pp. 397-407
Author(s):  
Juhani Karhumäki
Keyword(s):  
Free Monoid

FINITELY BASED WORDS

2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR
Keyword(s):  
Sufficient Conditions ◽  
Basis Property ◽  
Free Monoid ◽  
Finite Basis ◽  
Finitely Based ◽  
Finite Basis Property ◽  
Letter Alphabet ◽  
Finite Language ◽  
Rees Quotient ◽  
The Ideal

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

scholarly journals Disjunctive languages on a free monoid

1977 ◽  
Vol 34 (2) ◽  
pp. 123-129 ◽  
Author(s):  
H.J. Shyr
Keyword(s):  
Free Monoid

Γ-LANGUAGES AND Γ-AUTOMATA

2021 ◽  
Vol 10 (9) ◽  
pp. 3185-3194
Author(s):  
Anjeza Krakulli
Keyword(s):  
Free Monoid ◽  
Standard Theory

The aim of this paper is to extend the notion of an automaton as a triple made of a set of states, a free monoid on some set, and an action of this monoid on the set of states, to the case where the free monoid is replaced by a free Γ-monoid, and the action is replaced by the action of this Γ-monoid on the set of states. We call the respective triple a Γ-automaton. This concept leads to another new concept, that of a Γ-language, which is a subset of a free Γ-monoid. Also, we define recognizable Γ-languages and prove that they are exactly those Γ-languages that are recognized by a finite Γ-automaton. In the end, in analogy with the standard theory, we relate the recognizability of a Γ-language with the concept of division of semigroups.

Basics

2018 ◽  
pp. 7-8
Author(s):  
Christophe Reutenauer
Keyword(s):  
Free Group ◽  
Free Groups ◽  
Free Monoid ◽  
Periodic Pattern ◽  
Infinite Words ◽  
Reduced Words

Definitions and basic results about words: alphabet, length, free monoid, concatenation, prefix, suffix, factor, conjugation, reversal, palindrome, commutative image, periodicity, ultimate periodicity, periodic pattern, infinite words, bi-infinite words, free groups, reduced words, homomorphisms, embedding of a free monoid in a free group, abelianization,matrix of an endomorphism, GL2(Z), SL2(Z).

scholarly journals On a problem of Barnes and Duncan

1991 ◽  
Vol 34 (2) ◽  
pp. 321-323
Author(s):  
R. G. McLean
Keyword(s):  
Banach Algebra ◽  
Free Monoid ◽  
Finite Dimensional ◽  
Image Position ◽  
Funct Anal

Consider the free monoid on a non-empty set P, and let R be the quotient monoid determined by the relations:Let R have its natural involution * in which each element of P is Hermitian. We show that the Banach *-algebra ℓ1(R) has a separating family of finite dimensional *-representations and consequently is *-semisimple. This generalizes a result of B. A. Barnes and J. Duncan (J. Funct. Anal.18 (1975), 96–113.) dealing with the case where P has two elements.

scholarly journals Congruences on free monoids and submonoids of polycyclic monoids

1993 ◽  
Vol 54 (2) ◽  
pp. 236-253 ◽  
Author(s):  
John Meakin ◽  
Mark Sapir
Keyword(s):  
Semigroup Theory ◽  
Free Monoid ◽  
Inverse Semigroups ◽  
Free Monoids ◽  
One To One

AbstractWe establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.

Free Monoid

2004 ◽  
pp. 155-155
Author(s):  
Steven Duplij ◽  
Steven Duplij ◽  
Paulius Miškinis ◽  
Steven Duplij ◽  
Allen Parks ◽  
...  
Keyword(s):  
Free Monoid
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