  It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$
states always has a shortest 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 $n \leq 4$,
and with bounds on the number of symbols for $n \leq 10$. Here we give the full
analysis for $n \leq 6$, without bounds on the number of symbols.
  For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as
for DFAs and find the maximal shortest synchronizing word lengths, exceeding
$(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on
three symbols with exponential shortest synchronizing word length, giving
significantly better bounds than earlier exponential constructions. We give a
transformation of this PFA to a PFA on two symbols keeping exponential shortest
synchronizing word length, yielding a better bound than applying a similar
known transformation.
