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LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
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STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Automatic presentations for finitely generated groups
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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For automatic structures, several logics have been shown decidable: first-order logic, its extension by the infinity quantifier, by modulo-counting quantifiers, and even by a restricted form of second-order quantification. We review these decidability proofs. As a new result, we determine the data, the expression, and the combined complexity of quantifier-classes for first-order logic. Finally, we also recall that first-order logic becomes elementary decidable for automatic structures of bounded degree.