On Szilard Languages of Labelled Insertion Grammars

Abstract

In this work we initiate the study of Szilard languages of labelled insertion grammars. It is well-known that there exist context-free languages which cannot be generated by any insertion grammar. We show that there exist some regular languages which cannot be Szilard language of any labelled insertion grammar. But any regular language can be given as a homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 1. Also, any context-free language can be obtained as a homomorphic image of Szilard language of a labelled insertion grammar of weight 2. We show that even though insertion grammars of weight 1 can generate only context-free languages, there exist some context-sensitive language which can be obtained as Szilard language of a labelled insertion grammar of weight 1. At the end we show that any recursively enumerable language can be characterized by the homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 5.