A Characterization of Consensus Solvability for Closed Message Adversaries

Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns

Discrete modes of social information processing predict individual behavior of fish in a group

Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an active mode in which they are sensitive to the swimming patterns of conspecifics, and a passive mode where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors behavior. At the group level, switching between active and passive modes is uncorrelated among fish, yet correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates, as well as to other species