2007
DOI: 10.1007/s00446-007-0040-2
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The computational power of population protocols

Abstract: We consider the model of population protocols introduced by Angluin et al. (Computation in networks of passively mobile finite-state sensors, pp. 290-299. ACM, New York, 2004), in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the family of all-pairs communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power o… Show more

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Cited by 251 publications
(340 citation statements)
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References 38 publications
(73 reference statements)
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“…Condition 2 defines L i to be configurations with an i-voter, so those in L i \ L 1−i unanimously vote i, and those in O i are stable ("stuck" in the set L i \ L 1−i ). Condition 3 states that from every configuration reachable from an initial configuration, a "correct" output stable configuration is reachable from there; this is the usual way of expressing stable computation [6,8]. The relationships between these sets are depicted in Figure 1.…”
Section: Symmetric Output-stable Decidersmentioning
confidence: 99%
See 1 more Smart Citation
“…Condition 2 defines L i to be configurations with an i-voter, so those in L i \ L 1−i unanimously vote i, and those in O i are stable ("stuck" in the set L i \ L 1−i ). Condition 3 states that from every configuration reachable from an initial configuration, a "correct" output stable configuration is reachable from there; this is the usual way of expressing stable computation [6,8]. The relationships between these sets are depicted in Figure 1.…”
Section: Symmetric Output-stable Decidersmentioning
confidence: 99%
“…Using a result from the theory of population protocols [3,4], it is known that error-free CRNs decide exactly the semilinear sets [6]. 4 We study the computational robustness of error-free CRNs under different output conventions.…”
Section: Introductionmentioning
confidence: 99%
“…Given probability ǫ ≤ 1/2 and parameter R = 4 logq(max(n, 1/ǫ)): after R silent iterations of the knockout loop (lines [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], there remains exactly one active node, with probability at least 1 − ǫ/2.…”
Section: Fast Terminationmentioning
confidence: 99%
“…Note that (f, g)-alliances also have applications in the field of population protocols [1], or server allocation in computer networks [8].…”
Section: Introductionmentioning
confidence: 99%