Emptiness of Stack Automata is NEXPTIME-complete: A Correction

TL;DR

This paper corrects a previous claim by demonstrating that the emptiness problem for stack automata recognizing collapsible pushdown stacks is NEXPTIME-complete, not PSPACE-complete as previously stated.

Contribution

It clarifies the computational complexity of the emptiness problem for stack automata on collapsible pushdown stacks, establishing NEXPTIME-completeness.

Findings

Emptiness problem for collapsible pushdown stack automata is NEXPTIME-complete.

Previous claim of PSPACE-completeness was incorrect.

Provides a corrected complexity classification for the problem.

Abstract

A saturation algorithm for collapsible pushdown systems was published in ICALP 2012. This work introduced a class of stack automata used to recognised regular sets of collapsible pushdown configurations. It was shown that these automata form an effective boolean algebra, have a linear time membership problem, and are equivalent to an alternative automata representation appearing in LICS 2010. It was also claimed that the emptiness problem for stack automata is PSPACE-complete. Unfortunately, this claim is not true. We show that the problem is in fact NEXPTIME-complete when the stacks being accepted are collapsible pushdown stacks, rather than the annotated stacks used in ICALP 2012.