Tree Adjoining Languages and Multipushdown Languages

Many families of grammars have been studied to extend the power of context-free grammars, while retaining the attractive properties of context-free languages. Some of these formalisms have been proved equivalent to tree adjoining grammars (tag), introduced by computational linguists to model natural languages. Another family of grammars, multidepth grammars, introduced for describing the syntax of programming languages, generates a hierarchy of languages, called k- pushdown languages (k-pdl), for k ≥ 1. Multidepth grammars are simpler than some other formalisms and have a very natural accepting device, called multipushdown automaton. Here we study the relationship of k-pdl with tal, the class of languages generated by tag. We prove that 2-pdl ⊂ tal ⊂ 3-pdl. Moreover, tal can be characterized exactly as the smallest full super-AFL that includes 2-pdl