Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits

Abstract

The author examines various counting measures on space bounded nondeterministic auxiliary pushdown machines. In the main theorem, it is shown how a NAuxPDA may be simulated efficiently by a uniform family of Boolean circuits, which preserve the number of accepting paths in the NAuxPDA as the number of accepting subtrees in the Boolean circuit. The techniques used simulate the NAuxPDA in a novel way by considering the height and reversal bounds of an AuxPDA. One of the highlights of the present work is an exact characterization of the important class DET. It is shown that DET is exactly the class of functions that can be computed as the difference between the outputs of two counting logspace machines.<>