Abstract
It is known that determinizing a nondeterministic input-driven pushdown automaton (NIDPDA) of size n results in the worst case in a machine of size \(2^{\Theta(n^2)}\) (R. Alur, P. Madhusudan, “Adding nesting structure to words”, J.ACM 56(3), 2009). This paper considers the special case of k-path NIDPDAs, which have at most k computations on any input. It is shown that the smallest deterministic IDPDA equivalent to a k-path NIDPDA of size n is of size Θ(n k). The paper also gives an algorithm for deciding whether or not a given NIDPDA has the k-path property, for a given k; if k is fixed, the problem is P-complete.
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Okhotin, A., Salomaa, K. (2014). Input-Driven Pushdown Automata with Limited Nondeterminism. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_9
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DOI: https://doi.org/10.1007/978-3-319-09698-8_9
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