Distributed Synthesis for Alternating-Time Logics

We generalize the distributed synthesis problem to the setting of alternating-time temporal logics. Alternating-time logics specify the game-like interaction between processes in a distributed system, which may cooperate on some objectives and compete on others. Our synthesis algorithm works for hierarchical architectures (in any two processes there is one that can see all inputs of the other process) and specifications in the temporal logics ATL, ATL*, and the alternating-time µ-calculus. Given an architecture and a specification, the algorithm constructs a distributed system that is guaranteed to satisfy the specification. We show that the synthesis problem for non-hierarchical architectures is undecidable, even for CTL specifications. Our algorithm is therefore a comprehensive solution for the entire range of specification languages from CTL to the alternating-time µ-calculus.

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