Exact descriptional complexity of determinization of input-driven pushdown automata
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911842151956480 |
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| author | Martynova, Olga |
| author_facet | Martynova, Olga |
| contents | 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 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(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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact descriptional complexity of determinization of input-driven pushdown automata Martynova, Olga Formal Languages and Automata Theory 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 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(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). |
| title | Exact descriptional complexity of determinization of input-driven pushdown automata |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2404.10516 |