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arXiv · 2404.10516

Exact descriptional complexity of determinization of input-driven pushdown automata

Olga Martynova
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Abstract

The number of states and stack symbols needed to determinize nondeterministic input-driven pushdown automata (NIDPDA) working over a fixed alphabet is determined precisely. It is proved that in the worst case exactly 2^{n^2} states are needed to determinize an n-state NIDPDA, and the proof uses witness automata with a stack alphabet \Gamma = {0,1} working on strings over a 4-symbol input alphabet (Only an asymptotic lower bound was known before in the case of a fixed alphabet). Also, the impact of NIDPDA determinization on the size of stack alphabet is determined precisely for the first time: it is proved that s(2^{n^2}-1) stack symbols are necessary in the worst case to determinize an n-state NIDPDA working over an input alphabet of size s+5 with s left brackets (The previous lower bound was only asymptotic in the number of states and did not depend on the number of left brackets).

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Olga Martynova. 2024-04-16. Exact descriptional complexity of determinization of input-driven pushdown automata. https://arxiv.org/abs/2404.10516

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