## 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

## transformation monoid

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 5 words.

## 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 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*.

## syntactic monoid

Overview page. Subjects: Computing.

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

## 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...

## 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.

## free semigroup

Overview page. Subjects: Computing.

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* ...

## discrete structure

Overview page. Subjects: Computing.

A set of discrete elements on which certain operations are defined. Discrete implies noncontinuous and therefore discrete sets include finite and countable sets but not uncountable sets...

## semiring

Overview page. Subjects: Computing.

A set *S* (containing a 0 and a 1) on which there are defined two dyadic operations that are denoted by + and • and that obey certain properties: the set *S*, regarded as a set with a zero on...

## Strongly involutive uninorm algebras

in** Journal of Logic and Computation**

June 2013; p ublished online June 2012 .

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

We investigate uninorm algebras satisfying a strong version of involutiveness. More precisely, we require that negation is an order reversing monoid isomorphism between the positive cone...

## ring

Overview page. Subjects: Computing.

*R* on which there are defined two dyadic operations, normally denoted by + (addition) and · or juxtaposition (multiplication). With respect to addition, *null...*