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.

We show that co-synthesis defined classically, with the processes A 1 and A 2 either collaborating or competing, does not capture desirable solutions. Instead, the proper formulation of co-synthesis is the one where process A 1 competes with A 2 but not at the price of violating Φ 1, and vice versa. We call this assume-guarantee synthesis and show that it can be solved by computing secure-equilibrium strategies. In particular, from mutual-exclusion requirements the assume-guarantee synthesis algorithm automatically computes Peterson’s protocol.


Critical Section Mutual Exclusion Winning Strategy Secure Strategy Proof Rule 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Thomas A. Henzinger
    • 1
    • 2
  1. 1.University of California, BerkeleyUSA
  2. 2.EPFLSwitzerland

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