@inproceedings{140e1c6d490a42e387755f8f463d649c,

title = "An efficient algorithm finds noticeable trends and examples concerning the {\v c}erny conjecture",

abstract = "A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan {\v C}erny had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n -1)2. He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state complete DFA. The examples of DFA with shortest synchronizing word of length (n -1)2 are relatively rare. To the {\v C}erny sequence were added in all examples of {\v C}erny, Piricka and Rosenauerova (1971), of Kari (2001) and of Roman (2004). By help of a program based on some effective algorithms, a wide class of automata of size less than 11 was checked. The order of the algorithm finding synchronizing word is quadratic for overwhelming majority of known to date automata. Some new examples of n-state DFA with minimal synchronizing word of length (n - 1) 2 were discovered. The program recognized some remarkable trends concerning the length of the minimal synchronizing word.",

keywords = "Algorithm, Complexity, Deterministic finite automaton, Synchronizing word, {\v C}erny conjecture",

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

year = "2006",

doi = "10.1007/11821069_68",

language = "אנגלית",

isbn = "3540377913",

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

publisher = "Springer Verlag",

pages = "789--800",

booktitle = "Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings",

address = "גרמניה",

note = "31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 ; Conference date: 28-08-2006 Through 01-09-2006",

}