Tree Adjoining Languages and Multipushdown Languages

Abstract.

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 .