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Mathematical structure
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating
Automatic_semigroup
groups to other structures. For instance, it generalizes naturally to automatic semigroups. Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio
Automatic_group
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such
Regular_semigroup
Families of certain algebraic structures
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying
Special_classes_of_semigroups
Mathematical structure that describes the dynamics in a Markovian open quantum system
Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first
Quantum_Markov_semigroup
Concept in mathematics
and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images
Free_monoid
Generalized function whose value is zero everywhere except at zero
easy to see that this generates a semigroup in some sense—it is not absolutely integrable and so cannot define a semigroup in the above strong sense. Many
Dirac_delta_function
paratopological groups are automatically topological groups. Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially
Paratopological_group
Mathematics term
constructed from a particular class of endomorphism of a free monoid. Every automatic sequence is morphic. Let f be an endomorphism of the free monoid A∗ on
Morphic_word
String rewriting system
introduced this notion hoping to solve the word problem for finitely presented semigroups. Only in 1947 was the problem shown to be undecidable— this result was
Semi-Thue_system
Study of abstract machines and automata
automata transformations or as semigroup homomorphisms, when the state space, S, of the automaton is defined as a semigroup Sg. Monoids are also considered
Automata_theory
Russian mathematician (1889 to 1961)
mathematician and textbook author who expanded group theory to include semigroups and other magmas. Sushkevich attended secondary school in Voronezh and
Anton_Sushkevich
Algebraic structure in mathematics
necessarily abelian) under addition; multiplication is associative (so N is a semigroup under multiplication); and multiplication on the right distributes over
Near-ring
Richard M. (2002). "Some relatives of automatic and hyperbolic groups". In Gomes, Gracinda M. S. (ed.). Semigroups, algorithms, automata and languages.
Rational_monoid
Automatic Control. 26 (2): 301–320. doi:10.1109/tac.1981.1102603. Helton, J. William (1978). "Orbit structure of the Mobius transformation semigroup action
H-infinity methods in control theory
H-infinity_methods_in_control_theory
French mathematician (born 1958)
Cambridge University Press 1992 with Dominique Bakry, Michel Ledoux Markov Semigroups at Saint Flour, Series Probability at Saint Flour, Springer Verlag 2012
Laurent_Saloff-Coste
∈ Δ ∗ {\displaystyle p\in \Delta ^{*}} if there exists a non-erasing semigroup morphism f : Δ ∗ → Σ ∗ {\displaystyle f:\Delta ^{*}\rightarrow \Sigma
Unavoidable_pattern
Theorem in combinatorics on words
theorem and some of its extensions". Dynamical Aspects of Automata and Semigroup Theories. Satellite Workshop of Highlights of AutoMathA. Retrieved 19
Cobham's_theorem
Undecidability theorem in group theory
a similar earlier result for semigroups by Andrey Markov, Jr., proved by analogous methods. It was also in the semigroup context that Markov introduced
Adian–Rabin_theorem
Type of topological space in mathematics
on 2015-09-10. Lawson, J.; Madison, B. (1974). "Quotients of k-semigroups". Semigroup Forum. 9: 1–18. doi:10.1007/BF02194829., p. 3 Breuckmann, Tomas;
Locally_compact_space
Berthé & Rigo (2010) p.177 Allouche, Jean-Paul; Shallit, Jeffrey (2003). Automatic Sequences: Theory, Applications, Generalizations. Cambridge University
Recurrent_word
Indian mathematician
Kalyan B. Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra. Comm. Math. Phys. 205 (1999), no. 2, 377–403
Kalyan_Bidhan_Sinha
Vector space in mathematics
B (which is always possible if B is finite-dimensional), then it is automatically a bialgebra. (B, ∇, η, Δ, ε) is a bialgebra over K if it has the following
Bialgebra
Richard M. (2002). "Some relatives of automatic and hyperbolic groups". In Gomes, Gracinda M. S. (ed.). Semigroups, algorithms, automata and languages.
Rational_set
Swedish mathematician
embedding was isotone. Rådström characterized the generators of continuous semigroups of sets as compact convex sets. Rådström's Ph.D. students included Per
Hans_Rådström
Locally compact topological group with an invariant averaging operation
Helv. 56: 581–598. doi:10.1007/bf02566228. Day, M. M. (1949). "Means on semigroups and groups". Bulletin of the American Mathematical Society. 55 (11): 1054–1055
Amenable_group
Magma obeying the Latin square property
multiplicative inverse Semigroup – an algebraic structure consisting of a set together with an associative binary operation Monoid – a semigroup with an identity
Quasigroup
Type of residuated Boolean algebra with extra structure
ISBN 9780444520135. Schein, Boris M. (1970) "Relation algebras and function semigroups", Semigroup Forum 1: 1–62 Schmidt, Gunther (2010). Relational Mathematics. Cambridge
Relation_algebra
Algebraic structure in linear algebra
field F is large enough to contain a zero of this polynomial (which automatically happens for F algebraically closed, such as F = C) any linear map has
Vector_space
Problem in finite group theory
Carl-Fredrik (2021), "The word problem for one-relation monoids: a survey", Semigroup Forum, 103 (2): 297–355, arXiv:2105.02853, doi:10.1007/s00233-021-10216-8
Word_problem_for_groups
Type of Monte Carlo algorithms for signal processing and statistical inference
Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups". ESAIM Probability & Statistics. 7: 171–208. doi:10.1051/ps:2003001.
Particle_filter
Arithmetic operation
continuous exponents. This is the starting point of the mathematical theory of semigroups. Just as computing matrix powers with discrete exponents solves discrete
Exponentiation
Decidable first-order theory of the natural numbers with addition
Retrieved 11 June 2006. Ginsburg, Seymour; Spanier, Edwin Henry (1966). "Semigroups, Presburger Formulas, and Languages" (PDF). Pacific Journal of Mathematics
Presburger_arithmetic
Relationship between two functors abstracting many common constructions
ring to the underlying rng. Adjoining an identity to a semigroup. Similarly, given a semigroup S, we can add an identity element and obtain a monoid by
Adjoint_functors
Differential equation exhibiting high rate of dissipation
}^{tA}\|_{2}} is extremely small. In other words, the flow is nearly a semigroup, and e t A {\displaystyle {\mathrm {e} }^{tA}} is "close to singular"
Stiff_equation
British mathematician
(1984). "Stochastic dilations of uniformly continuous completely positive semigroups". Acta Applicandae Mathematicae. 2 (3–4): 353–378. doi:10.1007/BF02280859
R._L._Hudson
Finite or infinite ordered list of elements
more elements of A, with the binary operation of concatenation. The free semigroup A+ is the subsemigroup of A* containing all elements except the empty
Sequence
Result of repeatedly applying a mathematical function
the full orbit: the monoid of the Picard sequence (cf. transformation semigroup) has generalized to a full continuous group. This method (perturbative
Iterated_function
Ring without nonzero zero divisors
domain if and only if n {\displaystyle n} is prime. A finite domain is automatically a finite field, by Wedderburn's little theorem. The quaternions form
Domain_(ring_theory)
History of a branch of mathematics
the 1930s, but in the 1940s he proved important embedding properties of semigroups into groups, studied the isomorphism problem of group rings, established
History_of_group_theory
Committee for Aeronautics Anne Lester Hudson, American expert in topological semigroups, mathematics educator, and mathematics competition coach Hilda Phoebe
List_of_women_in_mathematics
Function between two metric spaces that only respects their large-scale geometry
the word is in his abstract for an AMS summer meeting in 1949, Means on semigroups and groups, Bull. A.M.S. 55 (1949) 1054–1055. Many text books on amenability
Quasi-isometry
Sapir – Russian-American mathematician working in geometric group theory, semigroup theory and combinatorial algebra, Centennial Professor of Mathematics
List of Vanderbilt University people
List_of_Vanderbilt_University_people
Feature of systems that defy description
Krohn–Rhodes complexity is an important topic in the study of finite semigroups and automata. In network theory, complexity is the product of richness
Complexity
Function from sets to numbers
of sets is modular. In geometry, a set function valued in some abelian semigroup that possess this property is known as a valuation. This geometric definition
Set_function
Algorithmic process of solving equations
has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative. But the same problem, viewed in
Unification (computer science)
Unification_(computer_science)
Ring that is also a vector space or a module
algebras Let A be an R-algebra. Any ring-theoretic ideal I in A is automatically an R-module since r · x = (r1A)x. This gives the quotient ring A / I
Associative_algebra
Semiring defined over probabilities
structure prediction, whenever a best hypothesis needs to be identified. Automatic speech recognition (ASR) heavily relies on the Viterbi semiring in decoding
Viterbi_semiring
Probabilistic problem-solving algorithms
Moral, Pierre; Miclo, Laurent (2002). "On the Stability of Non Linear Semigroup of Feynman-Kac Type" (PDF). Annales de la Faculté des Sciences de Toulouse
Mean-field_particle_methods
Algebraic structure
more complicated. For example, all ideals in a commutative ring are automatically two-sided, which simplifies the situation considerably. For a ring R
Commutative_ring
Musical artist
dissertations, mainly in the fields of representation of temporal groups and semigroups, machine learning and human-machine hybrid composition, non-linear cognitive
Gabriel_Pareyon
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
Boy/Male
Muslim/Islamic
Aromatic
Girl/Female
Muslim/Islamic
Aromatic
Boy/Male
Muslim
Aromatic
Girl/Female
Arabic, Muslim
Aromatic
Boy/Male
Arabic, Muslim
Fragrant; Aromatic
Girl/Female
Indian
Flower, Kind of aromatic plant
Girl/Female
Latin
Fortuna.
Girl/Female
Muslim
Aromatic
Girl/Female
Arabic, Muslim
Aromatic; Sweet Basil
Girl/Female
Arabic, Australian, Muslim
Kind of Aromatic Plant
Girl/Female
Muslim
Flower, Kind of aromatic plant
Girl/Female
Indian
Aromatic, A narrator of Hadith
Girl/Female
Arabic, French, Muslim
Aromatic
Boy/Male
Indian
Aromatic
Girl/Female
Afghan, Arabic, Australian
Aromatic; Sweet Basil
Girl/Female
Muslim
Flower, Kind of aromatic plant
Girl/Female
Arabic, Muslim
Aromatic Sweet Basil
Girl/Female
Muslim/Islamic
Aromatic
Girl/Female
Muslim
Aromatic, A narrator of Hadith
Girl/Female
Arabic, Muslim
Aromatic; Rare Moon
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
Boy/Male
Tamil
Noble, Wise, Faultless, Transparent
Boy/Male
Hindu, Indian
Servant of Lord Rama
Male
Chinese
great splendour.
Girl/Female
Indian, Punjabi, Sikh
In Service of the Original One
Male
Esperanto
Pet form of Esperanto Vilhelmo, VILCHJO means "will-helmet."
Girl/Female
Muslim
Pendant
Female
Spanish
Spanish pet form of Latin Susana, SUSANITA means "lily."
Boy/Male
Hindu, Indian
An Arrow; A Dart
Girl/Female
Indian
Victorious
Boy/Male
Hindu
Excellent
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
AUTOMATIC SEMIGROUP
v. i.
Any thing or being regarded as having the power of spontaneous motion or action.
a.
Not voluntary; not depending on the will; mechanical; as, automatic movements or functions.
n.
An apparatus for automatic ignition.
n.
The state or quality of being automatic; the power of self-moving; automatic, mechanical, or involuntary action. (Metaph.) A theory as to the activity of matter.
a.
Aromatic.
a.
Having an inherent power of action or motion.
n.
A person affected with asthma.
a.
Automatic.
a.
Alt. of Autocratical
a.
Alt. of Automatical
a.
Alt. of Asthmatical
v. i.
A self-moving machine, or one which has its motive power within itself; -- applied chiefly to machines which appear to imitate spontaneously the motions of living beings, such as men, birds, etc.
pl.
of Automaton
a.
Pertaining to, or produced by, an automaton; of the nature of an automaton; self-acting or self-regulating under fixed conditions; -- esp. applied to machinery or devices in which certain things formerly or usually done by hand are done by the machine or device itself; as, the automatic feed of a lathe; automatic gas lighting; an automatic engine or switch; an automatic mouse.
a.
Of or pertaining to a stoma; of the nature of a stoma.
n.
A medicine for diseases of the mouth.
a.
Alt. of Autoptical
pl.
of Automaton
adv.
In an automatic manner.
a.
Alt. of Axiomatical