113 research outputs found
Slowly synchronizing automata and digraphs
We present several infinite series of synchronizing automata for which the
minimum length of reset words is close to the square of the number of states.
These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure
A Note on a Recent Attempt to Improve the Pin-Frankl Bound
We provide a counterexample to a lemma used in a recent tentative improvement
of the the Pin-Frankl bound for synchronizing automata. This example naturally
leads us to formulate an open question, whose answer could fix the line of
proof, and improve the bound.Comment: Short note presenting a counterexample and the resulting open
questio
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