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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