  In this paper, we propose an approach for modeling and analysis of a number
of phenomena of collective behavior. By collectives we mean multi-agent systems
that transition from one state to another at discrete moments of time. The
behavior of a member of a collective (agent) is called conforming if the
opinion of this agent at current time moment conforms to the opinion of some
other agents at the previous time moment. We presume that at each moment of
time every agent makes a decision by choosing from the set {0,1} (where
1-decision corresponds to action and 0-decision corresponds to inaction). In
our approach we model collective behavior with synchronous Boolean networks. We
presume that in a network there can be agents that act at every moment of time.
Such agents are called instigators. Also there can be agents that never act.
Such agents are called loyalists. Agents that are neither instigators nor
loyalists are called simple agents. We study two combinatorial problems. The
first problem is to find a disposition of instigators that in several time
moments transforms a network from a state where a majority of simple agents are
inactive to a state with a majority of active agents. The second problem is to
find a disposition of loyalists that returns the network to a state with a
majority of inactive agents. Similar problems are studied for networks in which
simple agents demonstrate the contrary to conforming behavior that we call
anticonforming. We obtained several theoretical results regarding the behavior
of collectives of agents with conforming or anticonforming behavior. In
computational experiments we solved the described problems for randomly
generated networks with several hundred vertices. We reduced corresponding
combinatorial problems to the Boolean satisfiability problem (SAT) and used
modern SAT solvers to solve the instances obtained.
