Reactive Control Improvisation
For system designers needing random behavior (e.g., fuzz testers, surveillance robots), this work enables automated synthesis with randomness guarantees, but the results are incremental as they extend existing control improvisation to reactive settings.
The paper introduces reactive control improvisation, a framework that adds randomness requirements to reactive synthesis while maintaining functional correctness. It provides polynomial-time algorithms for reachability/safety games and deterministic automata, and polynomial-space algorithms for temporal logic specifications, showing no increase in complexity over non-randomized variants.
Reactive synthesis is a paradigm for automatically building correct-by-construction systems that interact with an unknown or adversarial environment. We study how to do reactive synthesis when part of the specification of the system is that its behavior should be random. Randomness can be useful, for example, in a network protocol fuzz tester whose output should be varied, or a planner for a surveillance robot whose route should be unpredictable. However, existing reactive synthesis techniques do not provide a way to ensure random behavior while maintaining functional correctness. Towards this end, we generalize the recently-proposed framework of control improvisation (CI) to add reactivity. The resulting framework of reactive control improvisation provides a natural way to integrate a randomness requirement with the usual functional specifications of reactive synthesis over a finite window. We theoretically characterize when such problems are realizable, and give a general method for solving them. For specifications given by reachability or safety games or by deterministic finite automata, our method yields a polynomial-time synthesis algorithm. For various other types of specifications including temporal logic formulas, we obtain a polynomial-space algorithm and prove matching PSPACE-hardness results. We show that all of these randomized variants of reactive synthesis are no harder in a complexity-theoretic sense than their non-randomized counterparts.