Experiments on Synchronizing Automata

Adam Roman
2010 Schedae Informaticae  
This work is motivated by theČerný Conjecture -an old unsolved problem in the automata theory. We describe the results of the experiments on synchronizing automata, which have led us to two interesting results. The first one is that the size of an automaton alphabet may play an important role in the issue of synchronization: we have found a 5-state automaton over a 3-letter alphabet which attains the upper bound from theČerný Conjecture, while there is no such automaton (exceptČerný automaton C
more » ... 5 ) over a binary alphabet. The second result emerging from the experiments is a theorem describing the dependencies between the automaton structure S expressed in terms of the so-called merging system and the maximal length of all minimal synchronizing words for automata of type S.
doi:10.2478/v10149-011-0003-z fatcat:zgjimoyrhfbvrnm6scinztf7wu