Learning Elementary Formal Systems and an Application to Discovering Motifs in Proteins

Proc. 2nd Workshop on Algorithmic Learning Theory, 139-150, 1991, Revised: April, 1993., Former version: Which classes of elementary formal systems are polynomial-time learnable, February, 1991An elementary formal system (EFS) is a logic program consisting of definite clauses whose arguments have patterns instead of first-order terms. We investigate EFSs for polynomial-time PAC-learnability and show by experiments on protein data that PAC-learning is very useful for discovering knowledge. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pattern in the head. With this new notion, we show that H-EFS (m, k, t, r) is polynomial- time learnable, which is the class of languages definable by EFSs consisting of at most m hereditary definite clauses with predicate symbols of arity at most $ ganmma $, where k and t bound the number of variable occurrences in the head and the number of atoms in the body, respectively. The class defined by all finite unions of EFSs in H-EFS(m, k, t, r) is also polynomial-time learnable. We also show an interesting series of NC-learnable classes of EFSs. As hardness results, the class of regular pattern languages is shown not polynomial-time learnable unless RP=NP. Furthermore, the related problem of deciding whether there is a common subsequence which is consistent with given positive and negative examples is shown NP-complete. As a practical application of our learning algorithm, we made experiments on learning transmembrane domains in proteins from amino acid sequences. The experimental results were quite successful