Chapter 18 Deep Pushdown Automata

Abstract

The present chapter defines deep pushdown automata, which represent a very natural modification of ordinary pushdown automata. While the ordinary versions can expand only the pushdown top, deep pushdown automata can make expansions deeper in the pushdown; otherwise, they both work identically. This chapter proves that the power of deep pushdown automata is similar to the generative power of regulated context-free grammars without erasing rules. Indeed, just like these grammars, deep pushdown automata are stronger than ordinary pushdown automata but less powerful than context-sensitive grammars. More precisely, they give rise to an infinite hierarchy of language families coinciding with the hierarchy resulting from n-limited state grammars. The present chapter is divided into two sections—Sects. 18.1 and 18.2. The former defines and illustrates deep pushdown automata. The latter establishes their accepting power, formulates some open problem areas concerning them, and suggests introducing new deterministic and generalized versions of these automata.