Abstract
Measures for the amount of ambiguity and nondeterminism in pushdown automata (PDA) are introduced. For every finite k, PDA's with ambiguity at most k are shown to accept exactly the class of languages generated by context-free grammars with ambiguity at most k. PDA's with an amount of nondeterminism at most k accept exactly the class of the unions of k deterministic context-free languages. For all finite or infinite k, k′ with k≤k′ there is a language, that can be accepted by a PDA with ambiguity k and nondeterminism k′ but by no PDA with less ambiguity or less nondeterminism. For every finite k, it is shown that the tradeoff from a description by a PDA with ambiguity k+1 and nondeterminism k+1 to PDA's with ambiguity k is bounded by no recursive function. The tradeoff from PDA's with ambiguity 1 and nondeterminism k+1 to PDA's with nondeterminism k also is bounded by no recursive function. The tradeoff from PDA's with branching k to PDA's with ambiguity k and branching k is at most exponential.
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© 1995 Springer-Verlag Berlin Heidelberg
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Herzog, C. (1995). Pushdown automata with bounded nondeterminism and bounded ambiguity. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_102
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DOI: https://doi.org/10.1007/3-540-59175-3_102
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