| Issue |
RAIRO-Theor. Inf. Appl.
Volume 42, Number 3, July-September 2008
JM'06
|
|
|---|---|---|
| Page(s) | 503 - 524 | |
| DOI | https://doi.org/10.1051/ita:2008014 | |
| Published online | 03 June 2008 | |
An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid
Dipartimento di Matematica e
Applicazioni, Università di Palermo, via Archirafi 34, 90123
Palermo, Italy; lgiambr;restivo@math.unipa.it
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 
has a given special property then 
where
for any submonoid L.
Mathematics Subject Classification: 68Q70 / 68Q45 / 20M35
Key words: Automata / free monoids / rank / intersection of submonoids
© EDP Sciences, 2008
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