### Abstract

We study the relative edit-distance problem between two input-driven languages. The relative edit-distance is closely related to the language inclusion problem, which is a crucial problem in formal verification. Input-driven languages are a robust subclass of context-free languages that enable to model program analysis questions within tractable time complexity. For instance, the language inclusion (or equivalence) problem is undecidable for context-free languages whereas the problem is solvable in polynomial time for input-driven languages specified by deterministic input-driven pushdown automata (IDPDAs) and is EXPTIME-complete for nondeterministic IDPDAs. Our main contribution is to prove that the relative edit-distance problem for two input-driven languages is decidable by designing a polynomial time IDPDA construction, based on the edit-distance, that recognizes a neighbourhood of a given input-driven language. In fact, the relative edit-distance problem between two input-driven languages turns out to be EXPTIME-complete when the neighbourhood distance threshold is fixed as a constant.

Original language | English |
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Title of host publication | Developments in Language Theory - 23rd International Conference, DLT 2019, Proceedings |

Editors | Piotrek Hofman, Michał Skrzypczak |

Publisher | Springer Verlag |

Pages | 127-139 |

Number of pages | 13 |

ISBN (Print) | 9783030248857 |

DOIs | |

Publication status | Published - 2019 |

Event | 23rd International Conference on Developments in Language Theory, DLT 2019 - Warsaw, Poland Duration: 2019 Aug 5 → 2019 Aug 9 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11647 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd International Conference on Developments in Language Theory, DLT 2019 |
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Country | Poland |

City | Warsaw |

Period | 19/8/5 → 19/8/9 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Developments in Language Theory - 23rd International Conference, DLT 2019, Proceedings*(pp. 127-139). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11647 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-24886-4_9