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This paper studies a variant of the \emph{leader election} problem under the\emph{stone age} model (Emek and Wattenhofer, PODC 2013) that considers anetwork of $n$ randomized finite automata with very weak communicationcapabilities (a multi-frequency asynchronous generalization of the\emph{beeping} model's communication scheme). Since solving the classic leaderelection problem is impossible even in more powerful models, we consider arelaxed variant, referred to as \emph{$k$-leader selection}, in which a leadershould be selected out of at most $k$ initial candidates. Our main contributionis an algorithm that solves $k$-leader selection for bounded $k$ in theaforementioned stone age model. On (general topology) graphs of diameter $D$,this algorithm runs in $\tilde{O}(D)$ time and succeeds with high probability.The assumption that $k$ is bounded turns out to be unavoidable: we prove thatif $k = \omega (1)$, then no algorithm in this model can solve $k$-leaderselection with a (positive) constant probability.

Selecting a Leader in a Network of Finite State Machines