Avoiding determinization

Automata on infinite objects are extensively used in system specification, verification, and synthesis. While some applications of the automata-theoretic approach have been well accepted by the industry, some have not yet been reduced to practice. Applications that involve determinization of automata on infinite words have been doomed to belong to the second category. This has to do with the intricacy of Safra 's optimal determinization construction, the fact that the state space that results from determinization is awfully complex and is not amenable to optimizations and a symbolic implementation, and the fact that determinization requires the introduction of acceptance conditions that are more complex than the Büchi acceptance condition. Examples of applications that involve determinization and belong to the unfortunate second category include model checking of ω-regular properties, decidability of branching temporal logics, and synthesis and control of open systems. We offer an alternative to the standard automatatheoretic approach. The crux of our approach is avoiding determinization. Our approach goes instead via universal co-Büchi automata. Like nondeterministic automata, universal automata may have several runs on every input. Here, however, an input is accepted if all of the runs are accepting. We show how the use of universal automata simplifies significantly known complementation constructions for automata on infinite words, known decision procedures for branching temporal logics, known synthesis algorithms, and other applications that are now based on determinization. Our algorithms are less difficult to implement and have practical advantages like being amenable to optimizations and a symbolic implementation.