Modifying the upper bound on the length of minimal synchronizing word
release_cbegzyooabe2hp5bi7lsqmozua
by
A. N. Trahtman
2012
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 Černy 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+6n-16)/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.
In text/plain
format
Archived Content
There are no accessible files associated with this release. You could check other releases for this work for an accessible version.
Know of a fulltext copy of on the public web? Submit a URL and we will archive it
1104.2409v5
access all versions, variants, and formats of this works (eg, pre-prints)