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arXiv · 1612.07881

On incomplete and synchronizing finite sets

Arturo Carpi·Flavio D'Alessandro
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Abstract

This paper situates itself in the theory of variable length codes and of finite automata where the concepts of completeness and synchronization play a central role. In this theoretical setting, we investigate the problem of finding upper bounds to the minimal length of synchronizing words and incompletable words of a finite language X in terms of the length of the words of X. This problem is related to two well-known conjectures formulated by Cerny and Restivo, respectively. In particular, if Restivo's conjecture is true, our main result provides a quadratic bound for the minimal length of a synchronizing pair of any finite synchronizing complete code with respect to the maximal length of its words.

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Arturo Carpi, Flavio D'Alessandro. 2016-12-23. On incomplete and synchronizing finite sets. https://arxiv.org/abs/1612.07881

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