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29 relations: Algebra, American Mathematical Society, Automata theory, Automaton, Biordered set, Cambridge University Press, Cayley's theorem, Closure (mathematics), Composition ring, DFA minimization, Finite group, Free monoid, Function (mathematics), Function composition, Group theory, Identity function, Krohn–Rhodes theory, Monoid, Oxford University Press, Permutation group, Regular language, Regular semigroup, Semigroup, Semigroup action, Special classes of semigroups, Symmetric group, Symmetric inverse semigroup, Syntactic monoid, Transformation (function).
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Automata theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
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Automaton
An automaton (plural: automata or automatons) is a self-operating machine, or a machine or control mechanism designed to automatically follow a predetermined sequence of operations, or respond to predetermined instructions.
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Biordered set
A biordered set ("boset") is a mathematical object that occurs in the description of the structure of the set of idempotents in a semigroup.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cayley's theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G; and the set of all such functions forms a group under function composition, called the symmetric group on G, and written as Sym(G).
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
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Composition ring
In mathematics, a composition ring, introduced in, is a commutative ring (R, 0, +, −, ·), possibly without an identity 1 (see non-unital ring), together with an operation such that, for any three elements f,g,h\in R one has.
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DFA minimization
In automata theory (a branch of computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states.
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Finite group
In abstract algebra, a finite group is a mathematical group with a finite number of elements.
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Free monoid
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Krohn–Rhodes theory
In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components.
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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.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).
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Regular language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be expressed using a regular expression, in the strict sense of the latter notion used in theoretical computer science (as opposed to many regular expressions engines provided by modern programming languages, which are augmented with features that allow recognition of languages that cannot be expressed by a classic regular expression).
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Regular semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a, there exists an element x such that axa.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semigroup action
In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations.
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Special classes of semigroups
In mathematics, a semigroup is a nonempty set together with an associative binary operation.
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Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
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Symmetric inverse semigroup
In abstract algebra, the set of all partial bijections on a set X (one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is \mathcal_X or \mathcal_X In general \mathcal_X is not commutative.
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Syntactic monoid
In mathematics and computer science, the syntactic monoid M(L) of a formal language L is the smallest monoid that recognizes the language L.
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Transformation (function)
In mathematics, particularly in semigroup theory, a transformation is a function f that maps a set X to itself, i.e..
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References
[1] https://en.wikipedia.org/wiki/Transformation_semigroup
