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Approximation of Reset Thresholds with Greedy Algorithms

Ananichev D. S., Gusev V. V.

Fundamenta Informaticae

2016

Vol. 145, nr 3

221--227

The problem of approximate computation of reset thresholds of synchronizing automata has gained a lot of attention recently. We introduce a broad class of algorithms that compute reset words and analyze their approximation ratios. We present three series of automata that reveal inherent limitations of greedy strategies for approximation of reset thresholds.

Principal Ideal Languages and Synchronizing Automata

Gusev V. V., Maslennikova M. I., Pribavkina E. V.

Fundamenta Informaticae

2014

Vol. 132, nr 1

95--108

We study ideal languages generated by a single word. We provide an algorithm to construct a strongly connected synchronizing automaton for which such a language serves as the language of synchronizing words. Also we present a compact formula to calculate the syntactic complexity of this language.