Abstract
It is known that converting an n-state nondeterministic nested word automaton (a.k.a. input-driven automaton; a.k.a. visibly pushdown automaton) to a corresponding deterministic automaton requires in the worst case \(2^{\Theta(n^2)}\) states (R. Alur, P. Madhusudan: Adding nesting structure to words, DLT’06). We show that the same worst case \(2^{\Theta(n^2)}\) size blow-up occurs when converting a nondeterministic nested word automaton to an unambiguous one, and an unambiguous nested word automaton to a deterministic one. In addition, the methods developed in this paper are used to demonstrate that the state complexity of complementation for nondeterministic nested word automata is \(2^{\Theta(n^2)}\), and that the state complexity of homomorphism for deterministic nested word automata is \(2^{\Theta(n^2)}\).
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Okhotin, A., Salomaa, K. (2011). Descriptional Complexity of Unambiguous Nested Word Automata. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_33
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