Stone duality and the recognisable languages over an algebra

Authors:
Mai Gehrke
Affiliations:
Radboud University Nijmegen, The Netherlands
Venue:
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Year:
2009

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Abstract

This is a theoretical paper giving the extended Stone duality perspective on the recently discovered connection between duality theory as studied in non-classical logic and theoretical computer science and the algebraic theory of finite state automata. As a bi-product we obtain a general result about profinite completion, namely, that it is the dual under extended Stone duality of the recognisable languages over the original algebra equipped with certain residuation operations.