Program schemes with deep pushdown storage.

Abstract

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, $\mbox{NPSDS}_s$, based around assignments, while-loops and non-deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of $\mbox{NPSDS}_s$ by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes {\bf NP} and {\bf PSPACE}. Furthermore, we show that all problems accepted by program schemes of $\mbox{NPSDS}_s$ are in {\bf EXPTIME}.