Abstract
We show that if the state set Q of a synchronizing automaton \( \mathcal{A} = \left\langle {Q,\sum ,\delta } \right\rangle \) admits a linear order such that for each letter a ∈ Σ the transformation δ(_, a) of Q preserves this order, then \( \mathcal{A} \) 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.
The authors acknowledge support from the Education Ministry of Russian Federation, grants E02-1.0-143 and 04.01.059, from the Russian Foundation of Basic Research, grant 01-01-00258, and from the INTAS through the Network project 99-1224 ‘Combinatorial and Geometric Theory of Groups and Semigroups and its Applications to Computer Science’.
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Ananichev, D.S., Volkov, M.V. (2003). Synchronizing Monotonic Automata. In: Ésik, Z., Fülöp, Z. (eds) Developments in Language Theory. DLT 2003. Lecture Notes in Computer Science, vol 2710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45007-6_8
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DOI: https://doi.org/10.1007/3-540-45007-6_8
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