Reactive Control Improvisation

TL;DR

This paper extends reactive synthesis to include randomness in system behavior, enabling the creation of correct and unpredictable reactive systems with a new framework called reactive control improvisation.

Contribution

It introduces reactive control improvisation, a framework that integrates randomness into reactive synthesis, with algorithms for various specification types and complexity analysis.

Findings

Polynomial-time algorithms for reachability, safety, and DFA specifications.

Polynomial-space algorithms and PSPACE-hardness for temporal logic specifications.

Randomized reactive synthesis problems are as computationally hard as their deterministic versions.

Abstract

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.