Pushdown automata with bounded nondeterminism and bounded ambiguity

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.