a School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050 South Africa
b Department of Computer Science, University of Stellenbosch, Private Bag X1, Matieland, 7602 South Africa
Abstract:
Random context grammars belong to the class of context-free grammars with regulated rewriting. Their productions depend on context that may be randomly distributed in a sentential form. Context is classified as either permitting or forbidding, where permitting context enables the application of a production and forbidding context inhibits it. For random context languages of finite index a generalization of the well-known pumping lemma for context-free languages has been proven. We drop the finite index restriction and concentrate on non-erasing grammars that use permitting context only. We prove a pumping lemma for their languages that generalizes and refines the existing one, and show that these grammars are strictly weaker than the non-erasing random context grammars.