On the Computational Complexity of Predicting Dynamical Evolution of Large Agent Ensembles

We study global behavior of large ensembles of simple reactive agents. We do so by applying computational complexity tools to the analysis of formal complex systems and their dynamics. Since we are interested in the global dynamics and emerging behavior of large agent ensembles, rather than in an individual agent’s deliberation, learning or other cognitive abilities, the discrete complex systems we study are based on the communicating finite state machine (CFSM) abstraction. In particular, we show that counting the number of possible evolutions of a particular class of CFSMs is computationally intractable, even when those CFSMs are very severely restricted both in terms of an individual agent’s behavior (that is, the local update rules), and the inter-agent interaction pattern (that is, the underlying communication network topology). We use this abstract framework to formally prove the well-known intuition about multi-agent systems (MAS) that a complex and, in general, unpredictable global behavior may arise from coupling of rather simple local behaviors and interactions.