2024/04/16 by Martynova, Olga
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2404.10516
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 2n2 states are needed to determinize an n-state NIDPDA, and the proof uses witness automata with a stack alphabet Γ= 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(2n2-1) 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).