## Abstract

The degree of ambiguity (respectively, the path size) of a nondeterministic automaton, on a given input, measures the number of accepting computations (respectively, the number of all computations). It is known that deciding the finiteness of the degree of ambiguity of a nondeterministic pushdown automaton is undecidable. Also, it is undecidable for a given k≥3 to decide whether the path size of a nondeterministic pushdown automaton is bounded by k. As the main result, we show that deciding the finiteness of the path size of a nondeterministic pushdown automaton can be done in polynomial time. Also, we show that the k-path problem for nondeterministic input-driven pushdown automata (respectively, for nondeterministic finite automata) is complete for exponential time (respectively, complete for polynomial space).

Original language | English |
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Pages (from-to) | 170-181 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 939 |

DOIs | |

Publication status | Published - 2023 Jan 4 |

### Bibliographical note

Funding Information:Han was supported by the IITP grants (2018-0-00276, 2020-0-01361).Ko was supported by the NRF grant (2020R1A4A3079947).Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Publisher Copyright:

© 2022 Elsevier B.V.

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)