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 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
Cerny-like problems for finite sets of words
CARPI, Arturo;
2014
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 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 wordsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
