PSSMs (Position-Specific Score Matrices) have been applied to various problems in Bioinformatics. We study the following problem: given positive examples (sequences) and negative examples (sequences), find a PSSM which correctly discriminates between positive and negative examples. We prove that this problem is solved in polynomial time if the size of a PSSM is bounded by a constant. On the other hand, we prove that this problem is NP-hard if the size is not bounded. We also prove similar results on deriving a mixture of PSSMs.