Entropy, Vol. 21, Pages 805: Integrated Information in Process-Algebraic Compositions (Entropy)

Integrated Information Theory (IIT) is most typically applied to Boolean Nets, a state transition model in which system parts cooperate by sharing state variables. By contrast, in Process Algebra, whose semantics can also be formulated in terms of (labeled) state transitions, system parts—“processes”—cooperate by sharing transitions with matching labels, according to interaction patterns expressed by suitable composition operators. Despite this substantial difference, questioning how much additional information is provided by the integration of the interacting partners above and beyond the sum of their independent contributions appears perfectly legitimate with both types of cooperation. In fact, we collect statistical data about ? —integrated information—relative to pairs of boolean nets that cooperate by three alternative mechanisms: shared variables—the standard choice for boolean nets—and two forms of shared transition, inspired by two process algebras. We name these mechanisms α , β and γ . Quantitative characterizations of all of them are obtained by considering three alternative execution modes, namely synchronous, asynchronous and “hybrid”, by exploring the full range of possible coupling degrees in all three cases, and by considering two possible definitions of ? based on two alternative notions of distribution distance.