Stone Duality and the Recognisable Languages over an Algebra
نویسنده
چکیده
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.
منابع مشابه
Stone duality, topological algebra, and recognition
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...
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