Experiments with Synchronizing Automata

We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to consider a number of conjectures and open questions concerning synchronizing automata, checking them for automata with a small number of states and discussing the results. In particular, we have verified the \v{C}ern\'y conjecture for all binary automata with at most 12 states, and all ternary automata with at most 8 states.