Abstract
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 a n the power of a in C. We show how we can construct C starting with factorizing codes C∼ with a n ∈ C∼ and n < n, under the hypothesis that all words a i waj 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 sufix 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.
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Partially supported by MURST Project “Unconventional Computational Models: Syntactic and Combinatorial Methods” - “Modelli di calcolo innovativi: Metodi sintattici e combinatory”.
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De Felice, C. (2000). Factorizing Codes and Schützenberger Conjectures. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_25
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DOI: https://doi.org/10.1007/3-540-44612-5_25
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