About: Krohn–Rhodes theory

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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. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade").

Attributes	Values
rdf:type	programming language
rdfs:label	Teori Krohn–Rhodes (in) Krohn–Rhodes theory (en) Teorema de Krohn-Rhodes (pt)
rdfs:comment	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. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade"). (en) Dalam matematika dan ilmu komputer, Teori Krohn-Rhodes (atau teori automata aljabar) adalah pendekatan untuk mempelajari semigroup terbatas dan yang berusaha untuk mendekomposisi mereka dalam istilah komponen dasar. Komponen-komponen ini sesuai dengan dan grup sederhana terbatas yang digabungkan bersama dalam cara bebas umpan balik (disebut "produk karangan bunga" atau "kaskade"). (in) Em matemática e na ciência da computação, o Teorema de Krohn-Rhodes (ou Teoria dos Autômatos Algebraica) é uma abordagem para o estudo dos semigrupos e automatas finitos que busca decompô-los em termos de componentes elementares. Esses componentes correspondem a semigrupos finitos aperiódicos e grupos simples finitos que são combinados de uma maneira livre de feedback (chamado de produtos coroa ou cascata). (pt)
dcterms:subject	Semigroup theory Finite automata Category theory
Wikipage page ID	513506 (xsd:integer)
Wikipage revision ID	1120254964 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Psychology Samuel Eilenberg Biology Deterministic finite automaton Algorithm Aperiodic semigroup Homomorphic Jordan–Hölder theorem International Journal of Algebra and Computation Semigroup action GAP computer algebra system Semigroup theory Massachusetts Institute of Technology Mathematics Simple group Game theory Monoid Conference on Implementation and Application of Automata Simple groups Subsemigroup Complexity Computer algebra system Computer science Fundamenta Informaticae Journal of Algebra Physics Subgroup Theoretical Computer Science (journal) Theory of Computing Systems Lecture Notes in Computer Science Semigroup Semigroup with three elements Finite automata Finite field Flip-flop (electronics) John Rhodes (mathematician) Journal of Pure and Applied Algebra Wreath product Harvard University Artificial intelligence Category theory Automata theory Green's relations Integer Category (mathematics) Category theory Triangular matrix Finite group Multiplication table Transformation semigroup Jordan–Hölder decomposition Transactions of the American Mathematical Society Finite automata Finite automaton Wiley–Interscience Information and Control Trivial (mathematics) dbr:Attila_Egri-Nagy_(computer_scientist) dbr:Chrystopher_L._Nehaniv_(mathematcian_and_computer_scientist) dbr:Frobenius–Lagrange_coordinates dbr:Kenneth_Krohn dbr:Sequential_machines
Link from a Wikipage to an external page	http://math.berkeley.edu/~rhodes/ https://archive.org/details/finiteautomatafo0000stra https://gap-packages.github.io/sgpdec/ https://www.complexityexplorer.org/tutorials/67-introduction-to-renormalization http://people.csail.mit.edu/meyer/remarks-on-algebraic-decomposition.pdf https://books.google.com/books%3Fhl=en&lr=&id=9n05BRVVQCwC&oi=fnd&pg=PA91&ots=Nfs7XGBmSm&sig=WCzauw8aN8dTP7K_aGrcODV0u34 https://books.google.com/books%3Fid=8L0QIEj0PI4C%7C https://books.google.com/books%3Fid=IgO0PQAACAAJ%7C https://books.google.com/books%3Fid=lj6zA1eaB8QC%7C http://uhra.herts.ac.uk/bitstream/2299/16600/2/900799.pdf https://www.complexityexplorer.org/tutorials/67-introduction-to-renormalization/segments/5426 https://www.ams.org/journals/tran/1965-116-00/S0002-9947-1965-0188316-1/S0002-9947-1965-0188316-1.pdf
sameAs	Krohn–Rhodes theory Krohn–Rhodes theory Krohn–Rhodes theory Krohn–Rhodes theory Krohn–Rhodes theory
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has abstract	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. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade"). Krohn and Rhodes found a general decomposition for finite automata. In doing their research, though, the authors discovered and proved an unexpected major result in finite semigroup theory, revealing a deep connection between finite automata and semigroups. (en)

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