Abstract
The states of a finite automaton are ordered by height. This order is shown to be graduated, and the well-known Cerny problem on the minimal length of reset words can be formulated in terms of global height. The problem is proved for automata with four states.
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Rystsov, I.K. On the Height of a Finite Automaton. Cybernetics and Systems Analysis 40, 467–477 (2004). https://doi.org/10.1023/B:CASA.0000047868.28366.da
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DOI: https://doi.org/10.1023/B:CASA.0000047868.28366.da