Symbolic construction of GR(1) contracts for synchronous systems with full information
This work addresses the problem of automatically synthesizing cooperative multi-agent specifications for systems with full information, providing a necessary condition and a symbolic method for constructing assumptions.
The paper proposes a symbolic algorithm to construct assume-guarantee contracts for multi-agent systems with GR(1) goals, ensuring cooperative realizability by generating weakly fair assumptions. It identifies circular dependencies in liveness goals as an obstruction and introduces nested games to address them, achieving polynomial time complexity in state space and linear in recurrence goals.
This work proposes a symbolic algorithm for the construction of assume-guarantee specifications that allow multiple agents to cooperate. Each agent is assigned goals expressed in a fragment of linear temporal logic known as generalized reactivity of rank 1 (GR(1)). These goals may be unrealizable, unless additional assumptions are made by each agent about the behavior of the other agents. The proposed algorithm constructs weakly fair assumptions for each agent, to ensure that they can cooperate successfully. A necessary requirement is that the given goals be cooperatively satisfiable. We prove that there exist games for which the GR(1) fragment with liveness properties over states is not sufficient to ensure realizability from any state in the cooperatively winning set. The obstruction is due to circular dependencies of liveness goals. To prevent circularity, we introduce nested games as a formalism to express specifications with conditional assumptions. The algorithm is symbolic, with fixpoint structure similar to the GR(1) synthesis algorithm, implying time complexity polynomial in the number of states, and linear in the number of recurrence goals.