An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 503-524.

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∩K has a given special property then rk ˜(H∩K)≤rk ˜(H)rk ˜(K) where rk ˜(L)=max(0,rk(L)-1) for any submonoid L.

DOI : 10.1051/ita:2008014
Classification : 68Q70, 68Q45, 20M35
Mots-clés : automata, free monoids, rank, intersection of submonoids 
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     author = {Giambruno, Laura and Restivo, Antonio},
     title = {An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {503--524},
     publisher = {EDP-Sciences},
     volume = {42},
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     year = {2008},
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     zbl = {1149.68058},
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     url = {http://archive.numdam.org/articles/10.1051/ita:2008014/}
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Giambruno, Laura; Restivo, Antonio. An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 503-524. doi : 10.1051/ita:2008014. http://archive.numdam.org/articles/10.1051/ita:2008014/

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