Complementing Emerson-Lei Elevator Automata (Technical Report)

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.