The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed number of interacting processes. In this work we look for the first time (to the best of our knowledge) at the problem of learning a distributed system with an arbitrary number of processes, assuming only that there exists a cutoff, i.e., a number of processes that is sufficient to produce all observable behaviors. Specifically, we consider fine broadcast protocols, these are broadcast protocols (BPs) with a finite cutoff and no hidden states. We provide a learning algorithm that can infer a correct BP from a sample that is consistent with a fine BP, and a minimal equivalent BP if the sample is sufficiently complete. On the negative side we show that (a) characteristic sets of exponential size are unavoidable, (b) the consistency problem for fine BPs is NP hard, and (c) that fine BPs are not polynomially predictable.

翻译：从示例中学习计算模型的问题正受到越来越多的关注。针对学习分布式系统模型这一尤其具有挑战性的问题，现有结果仅限于具有固定数量交互进程的模型。在这项工作中，我们首次（据我们所知）探讨了学习具有任意数量进程的分布式系统的问题，仅假设存在一个截止点，即足以产生所有可观测行为的进程数量。具体而言，我们考虑精细广播协议，即具有有限截止点且无隐藏状态的广播协议（BPs）。我们提出了一种学习算法，可从与精细BP一致的样本中推断出正确的BP，并在样本足够完整时推断出最小等价BP。在消极方面，我们证明：（a）指数大小的特征集是不可避免的；（b）精细BP的一致性问题是NP难的；（c）精细BP不可多项式预测。