### Abstract

A distance between two languages is a useful tool to measure the language similarity, and is closely related to the intersection problem as well as the shortest string problem. A parsing expression grammar (PEG) is an unambiguous grammar such that the choice operator selects the first matching in PEG while it can be ambiguous in a context-free grammar. PEGs are also closely related to top-down parsing languages. We consider two problems on parsing expression languages (PELs). One is the r-shortest string problem that decides whether or not a given PEL contains a string of length shorter than r. The other problem is the edit-distance problem of PELs with respect to other language families such as finite languages or regular languages. We show that the r-shortest string problem and the edit-distance problem with respect to finite languages are NEXPTIME-complete, and the edit-distance problem with respect to regular languages is undecidable. In addition, we prove that it is impossible to compute a length bound B(G) of a PEG G such that L(G) has a string w of length at most B(G).

Original language | English |
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Title of host publication | Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings |

Editors | Nataša Jonoska, Dmytro Savchuk |

Publisher | Springer |

Pages | 43-54 |

Number of pages | 12 |

ISBN (Print) | 9783030485153 |

DOIs | |

Publication status | Published - 2020 |

Event | 24th International Conference on Developments in Language Theory, DLT 2020 - Tampa, United States Duration: 2020 May 11 → 2020 May 15 |

### 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 | 12086 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International Conference on Developments in Language Theory, DLT 2020 |
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Country | United States |

City | Tampa |

Period | 20/5/11 → 20/5/15 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings*(pp. 43-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12086 LNCS). Springer. https://doi.org/10.1007/978-3-030-48516-0_4