Exact descriptional complexity of determinization of input-driven pushdown automata
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).
Keywords
Cite
@article{arxiv.2404.10516,
title = {Exact descriptional complexity of determinization of input-driven pushdown automata},
author = {Olga Martynova},
journal= {arXiv preprint arXiv:2404.10516},
year = {2024}
}