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Additional
monoid
English Wikipedia - The Free Encyclopedia
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Monoid
In
abstract algebra
, a branch of
mathematics
, a
monoid
is an
algebraic structure
with a single
associative
binary operation
and an
identity element
. Monoids are studied in
semigroup
theory as they are semigroups with identity. Monoids occur in several branches of mathematics; for instance, they can be regarded as
categories
with a single
object
. Thus, they capture the idea of
function composition
within a set. Monoids are also commonly used in
computer science
, both in its foundational aspects and in practical programming. The set of
strings
built from a given set of
characters
is a
free monoid
. The
transition monoid
and
syntactic monoid
are used in describing
finite state machines
, whereas
trace monoids
and
history monoids
provide a foundation for
process calculi
and
concurrent computing
. Some of the more important results in the study of monoids are the
Krohn–Rhodes theorem
and the
star height problem
. The history of monoids, as well as a discussion of additional general properties, are found in the article on
semigroups
.
See more at Wikipedia.org...
© This article uses material from
Wikipedia
®
and is licensed under the
GNU Free Documentation License
and under the
Creative Commons Attribution-ShareAlike License
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monoid
domino
Free English-Vietnamese Dictionary
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monoid
monoid
monoit; nửa nhóm
augmented m. nửa nhóm được bổ sung
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