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arXiv · 1801.00742

Large Flocks of Small Birds: On the Minimal Size of Population Protocols

Michael Blondin·Javier Esparza·Stefan Jaax
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Abstract

Population protocols are a well established model of distributed computation by mobile finite-state agents with very limited storage. A classical result establishes that population protocols compute exactly predicates definable in Presburger arithmetic. We initiate the study of the minimal amount of memory required to compute a given predicate as a function of its size. We present results on the predicates $x \geq n$ for $n \in \mathbb{N}$, and more generally on the predicates corresponding to systems of linear inequalities. We show that they can be computed by protocols with $O(\log n)$ states (or, more generally, logarithmic in the coefficients of the predicate), and that, surprisingly, some families of predicates can be computed by protocols with $O(\log\log n)$ states. We give essentially matching lower bounds for the class of 1-aware protocols.

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Michael Blondin, Javier Esparza, Stefan Jaax. 2018-01-02. Large Flocks of Small Birds: On the Minimal Size of Population Protocols. https://doi.org/10.4230/lipics.stacs.2018.16

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