Leftist grammars and the Chomsky hierarchy

Leftist grammars can be characterized in terms of rules of the form a -> ba and cd -> d, without distinction between terminals and nonterminals. They were introduced by Motwani et. al. [9], where the accessibility problem for some general protection system was related to the membership problem of these grammars. This protection system was originally proposed in [3,10] in the context of Java virtual worlds. We show that the set of languages defined by general leftist grammars is not included in CFL, answering in negative a question from [9]. Moreover, we relate some restricted but naturally defined variants of leftist grammars to the language classes of the Chomsky hierarchy.