A free monoid containing all strongly Bi-singular languages and non-primitive words

2019 ◽  
Vol 4 (1) ◽  
pp. 57-66
Author(s):  
Chunhua Cao ◽  
Ling Li ◽  
Di Yang
Keyword(s):  
Free Monoid ◽  
Primitive Words

Non-primitive words of the formpqm

2017 ◽  
Vol 51 (3) ◽  
pp. 141-166 ◽  
Author(s):  
Othman Echi
Keyword(s):  
Primitive Words

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

scholarly journals On a special class of primitive words

2010 ◽  
Vol 411 (3) ◽  
pp. 617-630 ◽  
Author(s):  
Elena Czeizler ◽  
Lila Kari ◽  
Shinnosuke Seki
Keyword(s):  
Special Class ◽  
Primitive Words

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.

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