Slowly synchronizing automata and digraphs
Dmitry S. Ananichev, Vladimir V. Gusev, Mikhail V. Volkov
TL;DR
This paper explores specific automata and digraphs where the shortest reset words are nearly quadratic in length, highlighting their connection to primitive digraphs with large exponents.
Contribution
Introduces new infinite series of automata with near-quadratic reset word lengths related to primitive digraphs with large exponents.
Findings
Reset word lengths close to the square of the number of states
Connection between automata and primitive digraphs with large exponent
Provides examples of automata with near-maximal reset lengths
Abstract
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.
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