  Motif searching is an important step in the detection of rare events
occurring in a set of DNA or protein sequences. One formulation of the problem
is known as (l,d)-motif search or Planted Motif Search (PMS). In PMS we are
given two integers l and d and n biological sequences. We want to find all
sequences of length l that appear in each of the input sequences with at most d
mismatches. The PMS problem is NP-complete. PMS algorithms are typically
evaluated on certain instances considered challenging. This paper presents an
exact parallel PMS algorithm called PMS8. PMS8 is the first algorithm to solve
the challenging (l,d) instances (25,10) and (26,11). PMS8 is also efficient on
instances with larger l and d such as (50,21). This paper also introduces
necessary and sufficient conditions for 3 l-mers to have a common d-neighbor.
