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Published in:
2011 | OriginalPaper | Chapter
Short 3-Collapsing Words over a 2-Letter Alphabet
Authors : Alessandra Cherubini, Achille Frigeri, Brunetto Piochi
Published in: Developments in Language Theory
Publisher: Springer Berlin Heidelberg
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Let
$\mathcal{A}=(Q,\Sigma,\delta)$
be a finite deterministic complete automaton.
$\mathcal{A}$
is called
k
-compressible if there is a word
w
∈ Σ
+
such that the image of the state set
Q
under the action of
w
has at most size |
Q
| −
k
, in such case the word
w
is called
k
-compressing for
$\mathcal{A}$
. A word
w
∈ Σ
+
is
k
-collapsing if it is
k
-compressing for each
k
-compressible automaton of the alphabet Σ and it is
k
-synchronizing if it is
k
-compressing for each
k
-compressible automaton with
k
+ 1 states (see [1,2] for details).