A NOTE ON FINITELY GENERATED SEMIGROUPS OF REGULAR LANGUAGES

2007 ◽  
Author(s):  
SERGEY AFONIN ◽  
ELENA KHAZOVA
Keyword(s):  
Regular Languages ◽  
Finitely Generated

ON THE STRUCTURE OF FINITELY GENERATED SEMIGROUPS OF UNARY REGULAR LANGUAGES

2010 ◽  
Vol 21 (05) ◽  
pp. 689-704
Author(s):  
SERGEY AFONIN ◽  
ELENA KHAZOVA
Keyword(s):  
Regular Languages ◽  
Finitely Generated ◽  
Commutative Semigroups ◽  
Rigid Structure ◽  
Letter Alphabet

The set of all regular languages is closed under concatenation and forms a monoid known as the monoid of regular languages. In this paper the structure of finitely generated subsemigroups of this monoid in case of one letter alphabet is investigated. We prove that finitely generated semigroups of regular languages over a one letter alphabet are Kleene, rational and thus automatic. It is already known that not all of finitely generated commutative semigroups are automatic, thus we may conclude that semigroups of unary regular languages have more rigid structure.

MEMBERSHIP AND FINITENESS PROBLEMS FOR RATIONAL SETS OF REGULAR LANGUAGES

2006 ◽  
Vol 17 (03) ◽  
pp. 493-506 ◽  
Author(s):  
SERGEY AFONIN ◽  
ELENA KHAZOVA
Keyword(s):  
Query Processing ◽  
Regular Language ◽  
Regular Languages ◽  
Finite Alphabet ◽  
Finitely Generated ◽  
Semistructured Databases ◽  
Rational Subset ◽  
Finite Set ◽  
Rational Sets

Let Σ be a finite alphabet. A set [Formula: see text] of regular languages over Σ is called rational if there exists a finite set [Formula: see text] of regular languages over Σ such that [Formula: see text] is a rational subset of the finitely generated semigroup [Formula: see text] with [Formula: see text] as the set of generators and language concatenation as a product. We prove that for any rational set [Formula: see text] and any regular language R ⊆ Σ* it is decidable (1) whether [Formula: see text] or not, and (2) whether [Formula: see text] is finite or not. Possible applications to semistructured databases query processing are discussed.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Learning Regular Languages from Positive Evidence

1998 ◽  
Author(s):  
Laura Firoiu ◽  
Tim Oates ◽  
Paul R. Cohen
Keyword(s):  
Regular Languages ◽  
Positive Evidence

Collectives of Automata in Finitely Generated Groups

2020 ◽  
Vol 108 (5-6) ◽  
pp. 671-678
Author(s):  
D. V. Gusev ◽  
I. A. Ivanov-Pogodaev ◽  
A. Ya. Kanel-Belov
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Groups

scholarly journals TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS – CORRIGENDUM

2016 ◽  
Vol 17 (4) ◽  
pp. 979-980
Author(s):  
Alberto Chiecchio ◽  
Florian Enescu ◽  
Lance Edward Miller ◽  
Karl Schwede
Keyword(s):  
Finitely Generated

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

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