An automata-theoretical characterization of the OI-hierarchy

Abstract

This paper gives an automata-theoretical characterization of the OI-hierarchy (Damm (1982), Engelfriet and Schmidt (1977), Wand (1975)). This hierarchy is generated by so-called level-n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n-iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n. The equivalence proof is given constructively, its method is illustrated using examples. By viewing level-n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.