## Abstract

A lambda term is linear if every bound variable occurs exactly once. The same constant may occur more than once in a linear term. It is known that higher-order matching in the linear lambda calculus is NP-complete (de Groote 2000), even if each unknown occurs exactly once (Salvati and de Groote 2003). Salvati and de Groote (2003) also claim that the interpolation problem, a more restricted kind of matching problem which has just one occurrence of just one unknown, is NP-complete in the linear lambda calculus. In this paper, we correct a flaw in Salvati and de Groote's (2003) proof of this claim, and prove that NP-hardness still holds if we exclude constants from problem instances. Thus, multiple occurrences of constants do not play an essential role for NP-hardness of higher-order matching in the linear lambda calculus.

Original language | English |
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Pages (from-to) | 235-249 |

Number of pages | 15 |

Journal | Lecture Notes in Computer Science |

Volume | 3467 |

Publication status | Published - 2005 Sep 26 |

Externally published | Yes |

Event | 16th International Conference on Term Rewriting and Applications, RTA 2005 - Nara, Japan Duration: 2005 Apr 19 → 2005 Apr 21 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)