Abstract
It was conjectured by Cerný in 1964, that a synchronizing DFA on n states always has a synchronizing word of length at most \((n-1)^2\), and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for \(n \le 4\), and with bounds on the number of symbols for \(n \le 10\). Here we give the full analysis for \(n \le 6\), without bounds on the number of symbols.
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