Inductive inference of monogenic pure context-free languages

A subclass of context-free languages, called pure context-free languages, which is generated by context-free grammar with only one type of symbol (i.e., terminals and nonterminals are not distinguished), is introduced and the problem of identifying from positive data a restricted class of monogenic pure context-free languages (mono-PCF languages, in short) is investigated. The class of mono-PCF languages is incomparable to the class of regular languages. In this paper we show that the class of mono-PCF languages is polynomial time identifiable from positive data. That is, there is an algorithm that, given a mono-PCF language L, identifies from positive data, a grammar generating L, called a monogenic pure context-free grammar (mono-PCF grammar, in short) satisfying the property that the time for updating a conjecture is bounded by O (N³), where AT is the sum of lengths of all positive data provided. This is in contrast with another result in this paper that the class of PCF languages is not identifiable in the limit from positive data.