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An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid
Published online by Cambridge University Press: 03 June 2008
Abstract
We investigate the intersection of two finitely generated submonoids
of the free monoid on a finite alphabet. To this purpose, we
consider automata that recognize such submonoids and we study the
product automata recognizing their intersection. By using automata
methods we obtain a new proof of a result of Karhumäki on the
characterization of the intersection of two submonoids of
rank two, in the case of prefix (or suffix) generators. In a more
general setting, for an arbitrary number of generators, we prove
that if H and K are two finitely generated submonoids generated
by prefix sets such that the product automaton associated to $H \cap
K$ has a given special property then $\widetilde{rk}(H \cap K) \leq
\widetilde{rk}(H) \widetilde{rk}(K)$
where
$\widetilde{rk}(L)=\max(0,rk(L)-1)$
for any submonoid L.
- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 503 - 524
- Copyright
- © EDP Sciences, 2008
References
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