Abstract
The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences.
We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an application, we finally derive some new properties of maximal uniquely decipherable codes.
Partially supported by Italian MURST Project of National Relevance “Linguaggi Formali e Automi: Metodi, Modelli e Applicazioni”.
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Béal, MP., Burderi, F., Restivo, A. (2007). Coding Partitions: Regularity, Maximality and Global Ambiguity. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_8
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DOI: https://doi.org/10.1007/978-3-540-73208-2_8
Publisher Name: Springer, Berlin, Heidelberg
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