Abstract
We reduce the problem of synchronization of an n-state automaton with letters of rank at most r < n to the problem of synchronization of an r-state automaton with constraints given by a regular language. Using this technique we construct a series of synchronizing n-state automata in which every letter has rank r < n and whose reset threshold is at least r 2 − r − 1 Moreover, if \(r > \frac{n}{2}\), such automata are strongly connected.
Supported by the Russian Foundation for Basic Research, grant 10-01-00793, and by the Presidential Program for young researchers, grant MK-266.2012.1. Author is also grateful to Erasmus Mundus Action 2 Partnerships — Triple I.
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Gusev, V.V. (2012). Synchronizing Automata of Bounded Rank. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_15
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DOI: https://doi.org/10.1007/978-3-642-31606-7_15
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