Environmentally-friendly GR(1) Synthesis

TL;DR

This paper introduces a new approach to reactive synthesis called non-conflictingness, ensuring system strategies allow environment fulfillment of its liveness requirements, with an algorithm that maintains the same complexity as traditional GR(1) synthesis.

Contribution

It proposes a novel non-conflictingness requirement in reactive synthesis and provides a 4-nested fixed point algorithm that guarantees environment fulfillment without increasing complexity.

Findings

The new algorithm produces non-conflicting strategies.

It maintains the same asymptotic complexity as standard GR(1).

Experimental results compare performance with traditional GR(1) synthesis.

Abstract

Many problems in reactive synthesis are stated using two formulas ---an environment assumption and a system guarantee--- and ask for an implementation that satisfies the guarantee in environments that satisfy their assumption. Reactive synthesis tools often produce strategies that formally satisfy such specifications by actively preventing an environment assumption from holding. While formally correct, such strategies do not capture the intention of the designer. We introduce an additional requirement in reactive synthesis, non-conflictingness, which asks that a system strategy should always allow the environment to fulfill its liveness requirements. We give an algorithm for solving GR(1) synthesis that produces non-conflicting strategies. Our algorithm is given by a 4-nested fixed point in the $\mu$-calculus, in contrast to the usual 3-nested fixed point for GR(1). Our algorithm ensures that, in every environment that satisfies its assumptions on its own, traces of the resulting implementation satisfy both the assumptions and the guarantees. In addition, the asymptotic complexity of our algorithm is the same as that of the usual GR(1) solution. We have implemented our algorithm and show how its performance compares to the usual GR(1) synthesis algorithm.