On some factorization problems | Zendy

Marcella Anselmo | Zendy; Clelia De Felice | Zendy; Antonio Restivo | Zendy

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On some factorization problems

Author(s) -

Marcella Anselmo,

Clelia De Felice,

Antonio Restivo

Publication year - 1997

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1105730621

Subject(s) - factorization , decidability , unary operation , property (philosophy) , class (philosophy) , regular language , combinatorics , mathematics , product (mathematics) , computer science , discrete mathematics , algebra over a field , algorithm , pure mathematics , automaton , theoretical computer science , artificial intelligence , philosophy , geometry , epistemology

We consider three notions of factorization arising in dierent frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X A is called factorizing if there exists a language Y A such that XY = A and the product is unambiguous. This is a decidable property for recognizable languages X. If we consider the particular case of unary alphabets, we prove that nite factorizing languages can be constructed by using Krasner factorizations. Moreover, we extend Krasner’s algorithm to factorizations of A n . We introduce a class of languages, the strong factorizing languages, which are related to the factorizing codes, introduced by

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