Experiments on Synchronizing Automata
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This work is motivated by the ˇCern´y 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 the ˇCern´y Conjecture, while there is no such automaton (except ˇCern´y automaton C5) 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.
08 - 07 - 2015
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