Abstract
A sequential automatic algebra is a structure of the type (A; f 1,..., f n ), where A is recognised by a finite automaton, and functions f 1, ..., f n are total operations on A that are computed by input-output automata. Our input-output automata are variations of Mealy automata. We study some of the fundamental properties of these algebras and provide many examples. We give classification results for certain classes of groups, Boolean algebras, and linear orders. We also introduce different classes of sequential automatic algebras and give separating examples. We investigate linear orders considered as sequential automatic algebras. Finally, we outline some of the basic properties of sequential automatic unary algebras.
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Brough, M., Khoussainov, B., Nelson, P. (2008). Sequential Automatic Algebras. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_9
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DOI: https://doi.org/10.1007/978-3-540-69407-6_9
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