A word w is called synchronizing （recurrent, reset, directable） word of deterministic finite automata （DFA） if w brings all states of the automaton to a unique state. According to the famous conjecture of Cerny fr...A word w is called synchronizing （recurrent, reset, directable） word of deterministic finite automata （DFA） if w brings all states of the automaton to a unique state. According to the famous conjecture of Cerny from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most （n - 1）2. The problem is still open. It will be proved that the Cerny conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state （n 〉 2） synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than （n - 1）2/2. The last important class of DFA involved and studied by Schutzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established.展开更多
文摘A word w is called synchronizing （recurrent, reset, directable） word of deterministic finite automata （DFA） if w brings all states of the automaton to a unique state. According to the famous conjecture of Cerny from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most （n - 1）2. The problem is still open. It will be proved that the Cerny conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state （n 〉 2） synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than （n - 1）2/2. The last important class of DFA involved and studied by Schutzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established.
