An Online Induction Algorithm for Internal Contextual Grammars Using Restarting Automata

Abstract

In this paper, we propose a new algorithm to induce an internal contextual grammar from positive examples using restarting automata. Motivation comes from, real-time systems which induce the target grammar within a deadline. In our algorithm, we deal with real time inputs which are generated by internal contextual grammar. Principally grammatical inference and grammar induction are considered equivalent but there is a slight difference, in this paper we concentrate on that difference. Here initially our algorithm will concentrate on grammatical Inference but at last it will be ended up with the concept of grammar induction. In order to induce the grammar, we first obtain insertion rules by scanning an input at a particular time unit. The insertion rules are converted into contextual rules. This set of contextual rules will be a guess about the grammar without taking care of over generalization. Further we will check the correctness of the contextual rules using restarting automata for the next input string and we update the rules based on need, that is called correction phase. After getting the final time-unit/deadline as an input, the algorithm executes some steps on the induced grammar to prune the over generalization of strings. It produces the final grammar for the strings which are given within the final time-unit.