Explorability in Pushdown Automata
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Bedi, Ayaan Lehtinen, Karoliina |
| author_facet | Bedi, Ayaan Lehtinen, Karoliina |
| contents | We study explorability, a measure of nondeterminism in pushdown automata, which generalises history-determinism. An automaton is k-explorable if, while reading the input, it suffices to follow k concurrent runs, built step-by-step based only on the input seen so far, to construct an accepting one, if it exists. We show that the class of explorable PDAs lies strictly between history-deterministic and fully nondeterministic PDAs in terms of both expressiveness and succinctness. In fact increasing explorability induces an infinite hierarchy: each level k defines a strictly more expressive class than level k-1, yet the entire class remains less expressive than general nondeterministic PDAs. We then introduce a parameterized notion of explorability, where the number of runs may depend on input length, and show that exponential explorability precisely captures the context-free languages. Finally, we prove that explorable PDAs can be doubly exponentially more succinct than history-deterministic ones, and that the succinctness gap between deterministic and 2-explorable PDAs is not recursively enumerable. These results position explorability as a robust and operationally meaningful measure of nondeterminism for pushdown systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explorability in Pushdown Automata Bedi, Ayaan Lehtinen, Karoliina Formal Languages and Automata Theory Computation and Language We study explorability, a measure of nondeterminism in pushdown automata, which generalises history-determinism. An automaton is k-explorable if, while reading the input, it suffices to follow k concurrent runs, built step-by-step based only on the input seen so far, to construct an accepting one, if it exists. We show that the class of explorable PDAs lies strictly between history-deterministic and fully nondeterministic PDAs in terms of both expressiveness and succinctness. In fact increasing explorability induces an infinite hierarchy: each level k defines a strictly more expressive class than level k-1, yet the entire class remains less expressive than general nondeterministic PDAs. We then introduce a parameterized notion of explorability, where the number of runs may depend on input length, and show that exponential explorability precisely captures the context-free languages. Finally, we prove that explorable PDAs can be doubly exponentially more succinct than history-deterministic ones, and that the succinctness gap between deterministic and 2-explorable PDAs is not recursively enumerable. These results position explorability as a robust and operationally meaningful measure of nondeterminism for pushdown systems. |
| title | Explorability in Pushdown Automata |
| topic | Formal Languages and Automata Theory Computation and Language |
| url | https://arxiv.org/abs/2511.04048 |