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arXiv · 0909.3790

On Carpi and Alessandro conjecture

M. V. Berlinkov
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Abstract

The well known open Černý conjecture states that each \san with $n$ states has a \sw of length at most $(n-1)^2$. On the other hand, the best known upper bound is cubic of $n$. Recently, in the paper \cite{CARPI1} of Alessandro and Carpi, the authors introduced the new notion of strongly transitivity for automata and conjectured that this property with a help of \emph{Extension} method allows to get a quadratic upper bound for the length of the shortest \sws. They also confirmed this conjecture for circular automata. We disprove this conjecture and the long-standing \emph{Extension} conjecture too. We also consider the widely used Extension method and its perspectives.

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M. V. Berlinkov. 2010-02-14. On Carpi and Alessandro conjecture. https://arxiv.org/abs/0909.3790

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