Synthesizing Processes and Schedulers from Temporal Specifications

We examine two closely related problems: synthesizing processes to satisfy temporal specifications of reactive systems, and the synthesis of a scheduler to interact with and control a group of processes in order to meet a specification. Processes communicate through shared and distributed variables, either synchronously or asynchronously. In the finite state case, processes and specifications are arbitrary ω-regular languages, and both synthesis problems are solvable in doubly exponential time and space. The framework we present is flexible enough to incorporate dense real time into the model of concurrency, thereby allowing us to study the synthesis of real-time processes and schedulers. Real-time implementability and scheduling are also doubly exponential.