Finitely inductive (Fl) sequences are a class of sequences, finite or infinite, which are amenable to a certain mathematical representation which has direct significance to pattern recognition and string matching. Pattern recognition using the Fl technique first transforms known patterns into function table(s) byfactoring, and then uses the function table(s) to match an input pattern byfollowing. Factoring is done off line and only once for each pattern. The sequential time for matching two sequences depends only upon the length of the input sequence. In this paper, we propose cost-optimal (i.e., efficient) parallel algorithms for Fl sequence processing. These algorithms include parallelfactoring and followingby bucket packing on an exclusive-read and exclusive-write (EREW), parallel random access machine (PRAM) model. The proposed algorithms also have implications to parallel integer sorting.