Learning of erasing primitive formal systems from positive examples

The present paper considers the learning problem of erasing primitive formal systems, PFSs for short, in view of inductive inference in Gold framework from positive examples. A PFS is a kind of logic program over strings called regular patterns, and consists of exactly two axioms of the forms p(π)← and p(τ)←p(x1),…,p(xn), where p is a unary predicate symbol, π and τ are regular patterns, and xis are distinct variables. A PFS is erasing or nonerasing according to allowing the empty string substitution for some variables or not. We investigate the learnability of the class of languages generated by the erasing PFSs satisfying a certain condition. We first show that the class has M-finite thickness. Moriyama and Sato showed that a language class with M-finite thickness is learnable if and only if there is a finite tell tale set for each language in the class. We then introduce a particular type of finite set of strings for each erasing PFS, and show that the set is a finite tell tale set of the language. These imply that the class is learnable from positive examples.