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On the Representation of Real Numbers Using Regular Languages

✍ Scribed by P. Lecomte; M. Rigo

Publisher
Springer
Year
2002
Tongue
English
Weight
238 KB
Volume
35
Category
Article
ISSN
1433-0490

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A regular language of the form UP' M' is called a single loop from the viewpoint of automata theory. It is known that every regular language can be expressed as (U,,,, U,L.;IV, )U F. where .4 is an index set, u,, ~1~ EX\*, c, EX~, i E A, and F is a finite set of words. This expression is called an s

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Then the entropy decreases strictly: ent(L W ) Β‘ ent(L). In this note we present a new proof of this fact, based on a method of Gromov, which avoids the Perron-Frobenius theory. This result applies to the regular languages of ΓΏnitely generated free groups and an additional application is presented.