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- In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a "canonical form" and can tell if two elements given in canonical words differ by a generator. More precisely, let G be a group and A be a finite set of generators. Then an automatic structure of G with respect to A is a set of finite-state automata:
* the word-acceptor, which accepts for every element of G at least one word in representing it;
* multipliers, one for each , which accept a pair (w1, w2), for words wi accepted by the word-acceptor, precisely when in G. The property of being automatic does not depend on the set of generators. (en)
- En mathématiques, un groupe automatique est un groupe décrit à l'aide d'automates finis. L'intérêt des groupes automatiques est que le problème du mot est décidable. C'est un cas particulier d'une structure automatique. (fr)
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- 6023 (xsd:nonNegativeInteger)
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- En mathématiques, un groupe automatique est un groupe décrit à l'aide d'automates finis. L'intérêt des groupes automatiques est que le problème du mot est décidable. C'est un cas particulier d'une structure automatique. (fr)
- In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a "canonical form" and can tell if two elements given in canonical words differ by a generator. More precisely, let G be a group and A be a finite set of generators. Then an automatic structure of G with respect to A is a set of finite-state automata: The property of being automatic does not depend on the set of generators. (en)
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- Automatic group (en)
- Groupe automatique (fr)
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