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Factorizing Codes and Schützenberger Conjectures

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

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.

Partially supported by MURST Project “Unconventional Computational Models: Syntactic and Combinatorial Methods” - “Modelli di calcolo innovativi: Metodi sintattici e combinatory”.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Universitá di Salerno, 84081, Baronissi(SA), Italy

    Clelia De Felice

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  1. Clelia De Felice
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Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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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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  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

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