  For a set of mulitple sequences, their patterns,Longest Common Subsequences
(LCS) and Shortest Common Supersequences (SCS) represent different aspects of
these sequences profile, and they can all be used for biological sequence
comparisons and analysis. Revealing the relationship between the patterns and
LCS,SCS might provide us with a deeper view of the patterns of biological
sequences, in turn leading to better understanding of them. However, There is
no careful examinaton about the relationship between patterns, LCS and SCS. In
this paper, we have analyzed their relation, and given some lemmas. Based on
their relations, a set of algorithms called the PALS (PAtterns by Lcs and Scs)
algorithms are propsoed to discover patterns in a set of biological sequences.
These algorithms first generate the results for LCS and SCS of sequences by
heuristic, and consequently derive patterns from these results. Experiments
show that the PALS algorithms perform well (both in efficiency and in accuracy)
on a variety of sequences. The PALS approach also provides us with a solution
for transforming between the heuristic results of SCS and LCS.
