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Sequential Automatic Algebras

  • Michael Brough
  • Bakhadyr Khoussainov
  • Peter Nelson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)

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.

Keywords

Boolean Algebra Linear Order Unary Algebra Regular Language Congruence Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Brough
    • 1
  • Bakhadyr Khoussainov
    • 1
  • Peter Nelson
    • 1
  1. 1.Department of Computer ScienceUniversity of Auckland 

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