Abstract:We consider two random walks evolving synchronously on a random out-regular graph of n vertices with bounded out-degree r ≥ 2, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with respect to the generation of the graph, the meeting time of the two walks is stochastically dominated by a geometric random variable of rate (1+o(1))n −1 , uniformly over their starting locations. Further, we prove that this upper bound is typically tight, i.e., it is also a lower boun… Show more
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