Sequential Automatic Algebras
نویسندگان
چکیده
A sequential automatic algebra is a structure of the type (A; f1, . . . , fn), where A is recognised by a finite automaton, and functions f1, . . . , fn are total operations on A that are computed by inputoutput 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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تاریخ انتشار 2008