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Abstract

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.

Keywords

Critical Section Mutual Exclusion Winning Strategy Secure Strategy Proof Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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