# The graph structure of a deterministic automaton chosen at random

@article{Cai2017TheGS, title={The graph structure of a deterministic automaton chosen at random}, author={Xing Shi Cai and Luc Devroye}, journal={Random Structures \& Algorithms}, year={2017}, volume={51} }

An n‐state deterministic finite automaton over a k‐letter alphabet can be seen as a digraph with n vertices which all have k labeled out‐arcs. Grusho (Publ Math Inst Hungarian Acad Sci 5 (1960), 17–61). proved that whp in a random k‐out digraph there is a strongly connected component of linear size, i.e., a giant, and derived a central limit theorem. We show that whp the part outside the giant contains at most a few short cycles and mostly consists of tree‐like structures, and present a new…

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