|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Modifying the upper bound on the length of minimal synchronizing word | | A.N. Trahtman
; | | Date: |
13 Apr 2011 | | Abstract: | A word $w$ is called synchronizing (recurrent, reset, magic, directable) word
of deterministic finite automaton (DFA) if $w$ sends all states of the
automaton to a unique state. In 1964 Jan v{C}erny found a sequence of n-state
complete DFA possessing a minimal synchronizing word of length $(n-1)^2$. He
conjectured that it is an upper bound on the length of such words for complete
DFA. Nevertheless, the best upper bound $(n^3-n)/6$ was found almost 30 years
ago. We reduce the upper bound on the length of the minimal synchronizing word
to $n(7n^2+12n-4)/48$. An implemented algorithm for finding synchronizing word
with restricted upper bound is described. The work presents the distribution of
all synchronizing automata of small size according to the length of an almost
minimal synchronizing word. | | Source: | arXiv, 1104.2409 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER