@inproceedings{cf85fb2b5b4e4ad281aea7ade06294a4,

title = "Synchronization of some DFA",

abstract = "A word ω is called synchronizing (recurrent, reset, directable) word of deterministic finite automaton (DFA) if ω brings all states of the automaton to an unique state. {\v C}ern{\'y} conjectured in 1964 that every nstate synchronizable automaton possesses a synchronizing word of length at most (n - 1)2. The problem is still open. It will be proved that the minimal length of synchronizing word is not greater than (n - 1)2/2 for every n-state (n > 2) synchronizable DFA with transition monoid having only trivial subgroups (such automata are called aperiodic). This important class of DFA accepting precisely star-free languages was involved and studied by Sch{\"u}tzenberger. So for aperiodic automata as well as for automata accepting only star-free languages, the {\v C}ern{\'y} conjecture holds true. Some properties of an arbitrary synchronizable DFA and its transition semigroup were established. http://www.cs.biu.ac.il/~trakht/syn.html",

keywords = "Aperiodic semigroup, Deterministic finite automata, Synchronization, {\v C}ern{\'y} conjecture",

author = "Trahtman, {A. N.}",

year = "2007",

language = "אנגלית",

isbn = "3540725032",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "234--243",

booktitle = "Theory and Applications of Models of Computation - 4th International Conference, TAMC 2007, Proceedings",

address = "גרמניה",

note = "4th International Conference on Theory and Applications of Models of Computation, TAMC 2007 ; Conference date: 22-05-2007 Through 25-05-2007",

}