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arXiv · 1604.02879

An Extremal Series of Eulerian Synchronizing Automata

Marek Szykuła·Vojtěch Vorel
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Abstract

We present an infinite series of $n$-state Eulerian automata whose reset words have length at least $(n^2-3)/2$. This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that $(n^2-3)/2$ also forms an upper bound for this class and we experimentally verify it for small automata by an exhaustive computation.

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Marek Szykuła, Vojtěch Vorel. 2016-08-03. An Extremal Series of Eulerian Synchronizing Automata. https://doi.org/10.1007/978-3-662-53132-7_31

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