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- Automatic_group abstract "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, i. e. 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 itmultipliers, 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.The concept of automatic groups generalizes naturally to automatic semigroups.".
- Automatic_group wikiPageID "4224977".
- Automatic_group wikiPageRevisionID "590414320".
- Automatic_group hasPhotoCollection Automatic_group.
- Automatic_group subject Category:Combinatorics_on_words.
- Automatic_group subject Category:Computability_theory.
- Automatic_group subject Category:Computational_group_theory.
- Automatic_group subject Category:Properties_of_groups.
- Automatic_group type Abstraction100002137.
- Automatic_group type Possession100032613.
- Automatic_group type PropertiesOfGroups.
- Automatic_group type Property113244109.
- Automatic_group type Relation100031921.
- Automatic_group comment "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, i. e. 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.".
- Automatic_group label "Automatic group".
- Automatic_group sameAs m.0bqxf4.
- Automatic_group sameAs Q4826571.
- Automatic_group sameAs Q4826571.
- Automatic_group sameAs Automatic_group.
- Automatic_group wasDerivedFrom Automatic_group?oldid=590414320.
- Automatic_group isPrimaryTopicOf Automatic_group.