2,376 research outputs found
Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
For the Bernoulli Matching model of sequence alignment problem we apply the
Bethe ansatz technique via an exact mapping to the 5--vertex model on a square
lattice. Considering the terrace--like representation of the sequence alignment
problem, we reproduce by the Bethe ansatz the results for the averaged length
of the Longest Common Subsequence in Bernoulli approximation. In addition, we
compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified
On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences
It is well known that, when normalized by n, the expected length of a longest
common subsequence of d sequences of length n over an alphabet of size sigma
converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele
regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to
do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma
and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin
Subsequence Automata with Default Transitions
Let be a string of length with characters from an alphabet of size
. The \emph{subsequence automaton} of (often called the
\emph{directed acyclic subsequence graph}) is the minimal deterministic finite
automaton accepting all subsequences of . A straightforward construction
shows that the size (number of states and transitions) of the subsequence
automaton is and that this bound is asymptotically optimal.
In this paper, we consider subsequence automata with \emph{default
transitions}, that is, special transitions to be taken only if none of the
regular transitions match the current character, and which do not consume the
current character. We show that with default transitions, much smaller
subsequence automata are possible, and provide a full trade-off between the
size of the automaton and the \emph{delay}, i.e., the maximum number of
consecutive default transitions followed before consuming a character.
Specifically, given any integer parameter , , we
present a subsequence automaton with default transitions of size
and delay . Hence, with we
obtain an automaton of size and delay . On
the other extreme, with , we obtain an automaton of size and delay , thus matching the bound for the standard subsequence
automaton construction. Finally, we generalize the result to multiple strings.
The key component of our result is a novel hierarchical automata construction
of independent interest.Comment: Corrected typo
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