Group presentations, formal languages and characterizations of one-counter groups
Theoretical Computer Science
Word Processing in Groups
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Automatic structures: overview and future directions
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Automatic Structures: Richness and Limitations
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Automatic Presentations for Cancellative Semigroups
Language and Automata Theory and Applications
Unary automatic graphs: An algorithmic perspective
Mathematical Structures in Computer Science
Theories of Automatic Structures and Their Complexity
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Automatic presentations for semigroups
Information and Computation
Theoretical Computer Science
Unary automatic graphs: an algorithmic perspective
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Where automatic structures benefit from weighted automata
Algebraic Foundations in Computer Science
Tree-Automatic well-founded trees
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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A structure is said to be computable if its domain can be represented by a set which is accepted by a Turing machine and if its relations can then be checked using Turing machines. Restricting the Turing machines in this definition to finite automata gives us a class of structures with a particularly simple computational structure; these structures are said to have automatic presentations. Given their nice algorithmic properties, these have been of interest in a wide variety of areas. An area of particular interest has been the classification of automatic structures. One of the prime examples under consideration has been the class of groups. We give a complete characterization in the case of finitely generated groups and show that such a group has an automatic presentation if and only if it is virtually abelian.