In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication by a generator. The concept of an automatic semigroup was generalized from automatic groups by Campbell et al. (2001)
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| - Automatic semigroup (en)
- Demi-groupe automatique (fr)
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| - En mathématiques et en informatique théorique, un demi-groupe automatique est un demi-groupe finiment engendré équipé de langages rationnels sur un alphabet représentant l'ensemble des générateurs.Un de ces langages détermine des « formes canoniques » des éléments du demi-groupe, les autres langages permettent de déterminer si deux formes canoniques peuvent se déduire l'une de l’autre par multiplication avec un générateur. (fr)
- In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication by a generator. The concept of an automatic semigroup was generalized from automatic groups by Campbell et al. (2001) (en)
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| - In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication by a generator. Formally, let be a semigroup and be a finite set of generators. Then an automatic structure for with respect to consists of a regular language over such that every element of has at least one representative in and such that for each , the relation consisting of pairs with is regular, viewed as a subset of (A# × A#)*. Here A# is A augmented with a padding symbol. The concept of an automatic semigroup was generalized from automatic groups by Campbell et al. (2001) Unlike automatic groups (see Epstein et al. 1992), a semigroup may have an automatic structure with respect to one generating set, but not with respect to another. However, if an automatic semigroup has an identity, then it has an automatic structure with respect to any generating set (Duncan et al. 1999). (en)
- En mathématiques et en informatique théorique, un demi-groupe automatique est un demi-groupe finiment engendré équipé de langages rationnels sur un alphabet représentant l'ensemble des générateurs.Un de ces langages détermine des « formes canoniques » des éléments du demi-groupe, les autres langages permettent de déterminer si deux formes canoniques peuvent se déduire l'une de l’autre par multiplication avec un générateur. (fr)
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