Population protocols are a class of algorithms for modeling distributed
computation in networks of finite-state agents communicating through pairwise
interactions. Their suitability for analyzing numerous chemical processes has
motivated the adaptation of the original population protocol framework to
better model these chemical systems. In this paper, we further the study of two
such adaptations in the context of solving approximate majority:
persistent-state agents (or catalysts) and spontaneous state changes (or
leaks).
Based on models considered in recent protocols for populations with
persistent-state agents, we assume a population with n catalytic input agents
and m worker agents, and the goal of the worker agents is to compute some
predicate over the states of the catalytic inputs. We call this model the
Catalytic Input (CI) model. For m=Θ(n), we show that computing the
parity of the input population with high probability requires at least
Ω(n2) total interactions, demonstrating a strong separation between the
CI model and the standard population protocol model. On the other hand, we show
that the simple third-state dynamics of Angluin et al. for approximate majority
in the standard model can be naturally adapted to the CI model: we present such
a constant-state protocol for the CI model that solves approximate majority in
O(nlogn) total steps with high probability when the input margin is
Ω(nlogn).
We then show the robustness of third-state dynamics protocols to the
transient leaks events introduced by Alistarh et al. In both the original and
CI models, these protocols successfully compute approximate majority with high
probability in the presence of leaks occurring at each step with probability
β≤O(nlogn/n), exhibiting a resilience to leaks
similar to that of Byzantine agents in previous works