Assume-Guarantee Synthesis

The classical synthesis problem for reactive systems asks, given a proponent process A and an opponent process B, to refine A so that the closed-loop system A||B satisfies a given specification Φ. The solution of this problem requires the computation of a winning strategy for proponent A in a game against opponent B. We define and study the co-synthesis problem, where the proponent A consists itself of two independent processes, A = A 1||A 2, with specifications Φ 1 and Φ 2, and the goal is to refine both A 1 and A 2 so that A 1||A 2||B satisfies Φ 1 ∧ Φ 2. For example, if the opponent B is a fair scheduler for the two processes A 1 and A 2, and Φ i specifies the requirements of mutual exclusion for A i (e.g., starvation freedom), then the co-synthesis problem asks for the automatic synthesis of a mutual-exclusion protocol.