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Rational set

In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid that contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra.

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Properties

McKnight's theoremFinitely generatedRecognizable subsetComplementFinite groups
8 related topics

Example

AlphabetWordsSemilinear sets
3 related topics

Definition

Finite setIdentity element
2 related topics

Rational relations and rational functions

Binary relation
1 related topics

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Properties

Rational relations and rational functions

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Rational set

Nodes30
Edges29
Triples34
Avg. degree1.93
Density0.066667
Components1

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Rational set

Top relations

related to References · 30
Rational set → Algebra, Automata, Automata Theory, Berlin/Boston, Chapter, Chapter IV, Commutative Monoids, Diekert, Discrete Algebraic Methods, Eilenberg, Gerhard, Gruyther GmbH, Hertrampf, ISBN, Jean-Éric Pin, Journal, Kufleitner, Lock-gray-alt-2, Lock-green, Lock-red-alt-2
related to Properties · 4
Rational set → McKnight's, RAT, Rational, This

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Important terminology

rational displaystyle monoid set sets finite automata subset subsets theory recognizable element closed product monoids union example algebra generated kleene

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Rational setrelated to PropertiesMcKnight's0.60section
Rational setrelated to PropertiesThis0.60section
Rational setrelated to PropertiesRational0.60section
Rational setrelated to PropertiesRAT0.60section
Rational setrelated to ReferencesLock-green0.60section
Rational setrelated to ReferencesLock-gray-alt-20.60section
Rational setrelated to ReferencesLock-red-alt-20.60section
Rational setrelated to ReferencesWikisource-logo0.60section
Rational setrelated to ReferencesDiekert0.60section
Rational setrelated to ReferencesVolker0.60section
Rational setrelated to ReferencesKufleitner0.60section
Rational setrelated to ReferencesManfred0.60section

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