Analysis Problems for Graphical Dynamical Systems: A Unified Approach Through Graph Predicates

We present a unified approach for studying the complexity of analysis problems for Synchronous Dynamical Systems (SyDSs), a class of graphical models for networked multiagent systems. Our approach uses predicates based on graph embeddings to capture many phase space properties of SyDSs studied in the literature and additional properties which have not been considered previously. Using this formalism, we develop general results to show that many analysis problems for SyDSs are computationally intractable. However, when the underlying graph of the given SyDS is treewidth bounded and the local functions are r-symmetric (for any fixed r), we show that even counting versions of analysis problems can be solved efficiently.