Abstract
A deterministic incomplete automaton
= 〈Q, Σ, δ〉 is partially monotonic if its state set Q admits a linear order such that each partial transformation δ(_, a) with a ∈ Σ preserves the restriction of the order to the domain of the transformation. We show that if
possesses an annihilator word w ∈ Σ* whose action is nowhere defined, then
is annihilated by a word of length \( \left| Q \right| + \left\lfloor {\frac{{\left| Q \right| - 1}} {2}} \right\rfloor \) and this bound is tight.
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Original Russian Text © D.S. Ananichev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 1, pp. 3–13.
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Ananichev, D.S. The annulation threshold for partially monotonic automata. Russ Math. 54, 1–9 (2010). https://doi.org/10.3103/S1066369X10010019
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DOI: https://doi.org/10.3103/S1066369X10010019