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, PDAs with ambiguity at most k are shown to accept exactly the class of languages generated by context-free grammars with ambiguity at most k. PDAs 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 PDAs with ambiguity k is bounded by no recursive function. The tradeoff from PDAs with ambiguity 1 and nondeterminism k + 1 to PDAs with nondeterminism k also is bounded by no recursive function. The tradeoff from PDAs with branching k to PDAs with ambiguity k and branching k is at most exponential.