Open AccessPositive varieties and infinite words
Author(s) -
Jean -éric Pin
Publication year - 1998
Publication title -
lecture notes in computer science
Language(s) - English
Resource type - Book series
SCImago Journal Rank - 0.249
H-Index - 400
eISSN - 1611-3349
pISSN - 0302-9743
ISBN - 3-540-64275-7
DOI - 10.1007/bfb0054312
Subject(s) - complement (music) , mathematics , intersection (aeronautics) , algebraic variety , variety (cybernetics) , characterization (materials science) , pure mathematics , algebraic number , discrete mathematics , algebra over a field , mathematical analysis , physics , statistics , optics , biochemistry , chemistry , complementation , engineering , gene , phenotype , aerospace engineering
Carrying on the work of Arnold, Pecuchet and Perrin, Wilke has obtained a counterpart of Eilenberg's variety theorem for finite and infinite words. In this paper, we extend this theory for classes of lan- guages that are closed under union and intersection, but not necessarily under complement. As an example, we give a purely algebraic charac- terization of various classes of recognizable sets defined by topological properties (open, closed, Fand G) or by combinatorial properties
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