Constructing Self-stabilizing Oscillators in Population Protocols
Population protocols (PPs) are a model of passive distributed systems in which a collection of finite-state mobile agents interact with each other to accomplish a common task. Unlike other works, which investigate their computation power, this paper throws light on an aspect of PPs as a model of chemical reactions. Motivated by the well-known BZ reaction that provides an autonomous chemical oscillator, we address the problem of autonomously generating an oscillatory execution from any initial configuration (i.e., in a self-stabilizing manner). For deterministic PPs, we show that the self-stabilizing leader election (SS-LE) and the self-stabilizing oscillator problem (SS-OSC) are equivalent, in the sense that an SS-OSC protocol is constructible from a given SS-LE protocol and vice versa, which unfortunately implies that (1) resorting to a leader is inevitable (although we seek a decentralized solution) and (2) n states are necessary to create an oscillation of amplitude n, where n is the number of agents (although we seek a memory-efficient solution). Aiming at reducing the space complexity, we present and analyze some randomized oscillatory PPs.
KeywordsPopulation protocol Self-stabilization Oscillatory behavior Leader election Distributed algorithm
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