## monoid

Overview page. Subjects: Computing.

A semigroup that possesses an identity element, *e*. If *S* is a semigroup on which there is defined a dyadic operation ∘, then *x* ∘ *e* = *e* ∘ *x* = *x*for all elements *x* in *S*. Monoids play an...

## monoid

Overview page. Subjects: Computing.

A semigroup that possesses an identity element, *e*. If *S* is a semigroup on which there is defined a dyadic operation ∘, then *x* ∘ *e* = *e* ∘ *x* = *x*for all elements *x* in *S*. Monoids play an...

## free monoid

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 156 words.

A particular kind of *monoid, usually involving *strings. Note first that *concatenation is an *associative operation...

## free monoid

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 145 words.

A particular kind of *monoid, usually involving *strings. Note first that *concatenation is an *

## free monoid

Overview page. Subjects: Computing.

A particular kind of monoid, usually involving strings. Note first that concatenation is an associative operation and also that, if Λ is the empty string, then Λ*w* = *w* = *w*Λ for all strings *w*null...

## monoid

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 63 words.

A *semigroup that possesses an *identity element, *e*. If *S* is a semigroup on which there is defined a ...

## monoid

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 59 words.

A *semigroup that possesses an *identity element, *e*. If *S* is a semigroup on which there

## A Geometric Characterization of Automatic Monoids

in** The Quarterly Journal of Mathematics**

September 2004; p ublished online September 2004 .

Journal Article. Subjects: Pure Mathematics. 0 words.

It is well known that automatic groups can be characterized using geometric properties of their Cayley graphs. Along the same line of thought, we provide a geometric characterization of...

## Solutions to Some Open Problems on Totally Ordered Monoids

in** Journal of Logic and Computation**

August 2010; p ublished online November 2008 .

Journal Article. Subjects: Computing; Logic. 0 words.

In this article, solutions to three open problems on ordered commutative monoids posed in Evans *et al.* (2001, *Semigroup forum*, 62, 249-278) [4] are presented. By an ordered monoid, we...

## syntactic monoid

Overview page. Subjects: Computing.

Of a formal language *L*. The semigroup of the minimal machine for *L*.

## syntactic monoid

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 18 words.

(of a formal language *L*) The *semigroup of the *minimal machine for *L*.

## transformation monoid

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 5 words.

## transformation monoid

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 5 words.

## syntactic monoid

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 15 words.

of a formal language *L*. The *semigroup of the *minimal machine for *L*.

## The Moduli Scheme of Affine Spherical Varieties with a Free Weight Monoid

in** International Mathematics Research Notices**

January 2016; p ublished online October 2015 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 18682 words.

We study Alexeev and Brion's moduli scheme [math] of affine spherical varieties with weight monoid [math] under the assumption that [math] is free. We describe the tangent space to [math]...

## Graded Leinster Monoids and Generalized Deligne Conjecture for 1-Monoidal Abelian Categories

in** International Mathematics Research Notices**

October 2018; p ublished online March 2017 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 30942 words.

**Abstract**

In our recent paper Shoikhet [47], a version of the “generalized Deligne conjecture” for abelian [math]-fold monoidal categories is proven. For [math]...

## The Class of Representable Ordered Monoids has a Recursively Enumerable, Universal Axiomatisation but it is Not Finitely Axiomatisable

in** Logic Journal of the IGPL**

March 2005; p ublished online March 2005 .

Journal Article. Subjects: Logic. 0 words.

An ordered monoid is a structure with an identity element (1′), a binary composition operator (;) and an antisymmetric partial order (≤), satisfying certain axioms. A representation of an...

## free semigroup

Overview page. Subjects: Computing.

A free monoid, but without the identity element. See also semigroup.

## free semigroup

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 15 words.

A *free monoid, but without the *identity element. *See also*
semigroup.

## free semigroup

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 13 words.

A *free monoid, but without the *identity element. *See also*
semigroup.

## transformation semigroup

Overview page. Subjects: Computing.

A semigroup consisting of a collection *C* of transformations of a set *S* into itself (see function), the dyadic operation ∘ being the composition of functions; it is essential that the set *C* ...