On some factorization problems
TL;DR: If the particular case of unary alphabets is considered, it is proved that nite factorizing languages can be constructed by using Krasner factorizations, and the algorithm extended to factorizations of A n is extended.
read more
Abstract: 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
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Constructing Finite Maximal Codes from Schützenberger Conjecture
Marcella Anselmo
- 04 Oct 2001
TL;DR: This work considers two families of possible languages S and presents a method of constructing C from (S, P), that is relied on the construction of right- and left-factors of a language, based on a combinatorial characterization of left- and right-factorizing languages.
2
A non-ambiguous decomposition of regular languages and factorizing codes
TL;DR: It is shown that it is decidableWhether Z is L-decomposable and whether Z is finitely L- decomposability, in the case Z and L are regular languages.
On a property of the factorizing codes
TL;DR: A description of the structure of the words in C∩a*(A\a)a*, a being a letter in A, is given by using a class of factorizations of the cyclic groups discovered by Hajos.
References
•Book
Automata, Languages, and Machines
Samuel Eilenberg
- 01 Mar 1974
TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.
2.5K
•Book
Combinatorics on words
M. Lothaire
- 28 Dec 1984
TL;DR: Perrin and Perrin this article showed that square free words and idempotent semigroups can be expressed in terms of free monoids, and the critical factorization theorem of Van der Waerden's theorem.
1.9K