Sky Is Not the Limit: Tighter Rank Bounds for Elevator Automata in B\"{u}chi Automata Complementation (Technical Report)

TL;DR

This paper introduces heuristics and techniques to tighten rank bounds in B"uchi automata complementation, reducing state space explosion and improving performance, especially for elevator automata, a common class in practice.

Contribution

The paper identifies elevator automata and develops new heuristics and data-flow analysis methods to refine rank bounds, enhancing automata complementation efficiency.

Findings

Significantly reduces state space in automata complementation.

Outperforms existing tools on benchmark sets.

Effective for elevator automata and related structures.

Abstract

We propose several heuristics for mitigating one of the main causes of combinatorial explosion in rank-based complementation of B\"{u}chi automata (BAs): unnecessarily high bounds on the ranks of states. First, we identify elevator automata, which is a large class of BAs (generalizing semi-deterministic BAs), occurring often in practice, where ranks of states are bounded according to the structure of strongly connected components. The bounds for elevator automata also carry over to general BAs that contain elevator automata as a sub-structure. Second, we introduce two techniques for refining bounds on the ranks of BA states using data-flow analysis of the automaton. We implement out techniques as an extension of the tool Ranker for BA complementation and show that they indeed greatly prune the generated state space, obtaining significantly better results and outperforming other state-of-the-art tools on a large set of benchmarks.