Complementing Emerson-Lei Elevator Automata (Technical Report)

2026-06-25

AI Summary

Complementation of Emerson–Lei automata has long lacked efficient algorithms, both theoretically and practically, particularly when dealing with complex acceptance conditions. This work introduces the Emerson–Lei elevator automaton model and presents the first efficient complementation algorithm tailored to this structure. By integrating structured automaton analysis, classification of strongly connected components, and targeted optimization strategies, the proposed method achieves asymptotically superior complexity compared to the best existing approaches. Experimental evaluation demonstrates that its implementation in the Spot tool significantly outperforms current state-of-the-art complementation techniques for general Emerson–Lei automata, offering both theoretical improvements and practical performance gains.

Abstract

Büchi elevator automata naturally appear in several areas of formal methods as a structural expressibly-equivalent subclass of Büchi automata where every strongly connected component is either deterministic or inherently weak. It was shown that this class contains the majority of Büchi automata generated in practical applications, including LTL model-checking and verification of hyperproperties. Moreover, the elevator subclass enables more efficient complementation and determinization algorithms than unrestricted Büchi automata. In this paper, we introduce Emerson-Lei elevator automata, which is a generalization of Büchi elevator automata to richer acceptance conditions. We provide a complementation algorithm with a significantly better asymptotic complexity than the best known algorithm for unrestricted Emerson-Lei automata. The practical efficiency of our algorithm is demonstrated by an experimental comparison with the popular state-of-the-art tool Spot. Our work is, to the best of our knowledge, the first step towards practical algorithms for complementing, determinizing, and testing universality and inclusion of Emerson-Lei automata with rich acceptance conditions.

Problem

• Emerson-Lei automata
• complementation
• elevator automata
• Büchi automata
• acceptance conditions

Innovation

• Emerson-Lei automata
• elevator automata
• complementation algorithm
• rich acceptance conditions
• formal verification