关于种群趋于无穷大时种群协议的收敛性
On the Convergence of Population Protocols When Population Goes to Infinity
摘要：
人口协议已被引入作为一个模型的传感器网络组成的非常有限的移动代理没有控制自己的运动。人口协议对应于一个匿名代理的集合，由有限自动机建模，这些代理通过使用某些规则更新它们的状态来彼此交互以执行计算。他们的计算能力已经调查了几个假设，但总是当限制到有限大小的人口。特别是，在原始模型中稳定可计算的谓词已经被描述为在Presburger算法中可定义的谓词。我们从数学上研究了当种群规模趋于无穷大时种群协议的收敛性。我们这样做的一般结果，我们说明通过一个特定的人口协议的例子，我们甚至获得了渐近发展。这个例子特别表明，当考虑一个巨大的人口假设时，这些协议似乎具有相当不同的计算能力。
英文摘要：
Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered.
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