Fast Learning from Strings of 2-Letter Rigid Grammars

It is well-known that certain classes of classical categorial grammars are learnable, within Gold’s paradigm of identification in the limit, from positive examples. In the search for classes which can be learned efficiently from strings, we study the class of 2-letter rigid grammars, which is the class of classical categorial grammars with an alphabet of two letters, each of which is assigned a single type. The (non-trivial) structure of this class of grammars is studied and it is shown that grammars in this class can be learned very efficiently. The algorithm given for solving this learning problem runs in time linear in the total length of the input strings. After seeing two or more strings in a language, the algorithm can determine precisely the (finite) set of grammars which can generate those strings.