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A word w over a finite alphabet Σ is n-collapsing if for an arbitrary deterministic finite automaton A = Q, Σ, δ, the inequality |δ(Q, w)| ≤ |Q| − n holds provided that |δ(Q, u)| ≤ |Q| − n for some word u ∈ Σ + (depending on A). We prove that the the property of being n-collapsing is algorithmically recognizable for any given positive integer n. We also(More)
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