RAIRO-Theor. Inf. Appl.
Volume 42, Number 3, July-September 2008JM'06
|Page(s)||503 - 524|
|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;firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.