Synchronizing monotonic automata

Synchronizing monotonic automata

We show that if the state set Q of a synchronizing automaton A = 〈 Q , Σ , δ 〉 admits a linear order such that for each letter a ∈ Σ the transformation δ ( _ , a ) of Q preserves this order, then A possesses a reset word of length | Q | - 1 . We also consider two natural generalizations of the notio...

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Veröffentlicht in:Theoretical computer science 2004-11, Vol.327 (3), p.225-239
Hauptverfasser: Ananichev, D.S., Volkov, M.V.
Format: Artikel
Sprache:eng
Schlagworte:
Interval rank of a word
Monotonic automata
Order preserving transformation
Rank of a word
Synchronizing automata
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Zusammenfassung:We show that if the state set Q of a synchronizing automaton A = 〈 Q , Σ , δ 〉 admits a linear order such that for each letter a ∈ Σ the transformation δ ( _ , a ) of Q preserves this order, then A possesses a reset word of length | Q | - 1 . We also consider two natural generalizations of the notion of a reset word and provide for them results of a similar flavour.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2004.03.068