Symmetry Breaking with Noisy Processes

Abstract

Biology and computer science intersect at the problem of symmetry breaking, which is relevant in both fields. Accordingly, in recent years, distributed algorithm theorists have studied symmetry breaking problems in models inspired by biology to help provide insight into the capabilities and constraints of this natural process. A potential shortcoming of these models, however, is that they execute distributed algorithms precisely as specified. In nature, where computation is often implemented by messy analog systems, this precision cannot necessarily be guaranteed. Motivated by this observation, in this paper we present a general method for injecting computational noise into any distributed system model that describes processes as interacting state machines. Our method captures noise as a force that can cause state machines to transition to the wrong state. We combine this formalization of noise with the beeping models that have been a popular target of recent work on bio-inspired symmetry breaking. We produce new upper and lower bounds for both single hop and multihop models---studying leader election in the former and the maximal independent set problem in the latter. These bounds introduce new techniques for achieving robustness to noise, and identify some fundamental limits in this pursuit. We argue that both our general approach and specific results can help advance the productive relationship between biology and algorithm theory.