Rational series and their languages
Rational series and their languages
Construction of a family of finite maximal codes
Theoretical Computer Science
A partial result about the factorization conjecture for finite variable-length codes
Discrete Mathematics
Synchronization and decomposability for a family of codes: part 2
Discrete Mathematics
Hajós factorizations and completion of codes
Theoretical Computer Science
Hajós factorizations of cyclic groups—a simpler proof of a characterization
Journal of Automata, Languages and Combinatorics
On some Schützenberger conjectures
Information and Computation
Theory of Codes
Sur l'application du theoreme de Suschkewitsch a l'etude des codes rationnets complets
Proceedings of the 2nd Colloquium on Automata, Languages and Programming
Une Famille Remarquable de Codes Indecomposables
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Constructing Finite Maximal Codes from Schützenberger Conjecture
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
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In this paper we mainly deal with factorizing codes C over A, i.e., codes verifying the famous still open factorization conjecture formulated by Schützenberger. Suppose A = {a,b} and denote an the power of a in C. We show how we can construct C starting with factorizing codes C′ with an′ ∈ C′ and n′ n, under the hypothesis that all words aiwaj in C, with w ∈ bA*b ∪ {b}, satisfy i, j n. The operation involved, already introduced in [1], is also used to show that all maximal codes C = P(A - 1)S + 1 with P, S ∈ Z(A) and P or S in Z(a) can be constructed by means of this operation starting from prefix and suffix codes. Inspired by another early Schützenberger conjecture, we propose here an open problem related to the results obtained and to the operation introduced in [1] and considered in this paper.