3 research outputs found
Efficient validation and construction of border arrays and validation of string matching automata
No full textWe present an on-line linear time and space algorithm
to check if an integer
array f is the border array of at least one string w built on a bounded
or unbounded size alphabet Σ.
First of all, we show a bijection between the border array of a string w
and the skeleton of the DFA recognizing Σ*ω,
called a string matching automaton (SMA).
Different strings can have the same border array but the originality
of the presented method is that the correspondence between a border array and
a skeleton of SMA is independent from the underlying strings.
This enables to design algorithms for validating and generating border
arrays that outperform existing ones.
The validating algorithm lowers the delay (maximal number of comparisons on
one element of the array)
from O(|w|) to 1 + min{|Σ|,1 + log2|ω|} compared to existing algorithms.
We then give results on the numbers of distinct border arrays depending on the
alphabet size.
We also present an algorithm that checks if a given directed unlabeled graph G
is the skeleton of a
SMA on an alphabet of size s in linear time.
Along the process the algorithm can build one string w for which G
is the SMA skeleton
