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Higher-Order Matching in the Linear Lambda Calculus in the Absence of Constants Is NP-Complete

  • Ryo Yoshinaka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3467)

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.

Keywords

Problem Instance Free Variable Interpolation Problem Atomic Type Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ryo Yoshinaka
    • 1
    • 2
  1. 1.Graduate School of Interdisciplinary Information StudiesUniversity of TokyoTokyoJapan
  2. 2.National Institute of InformaticsTokyoJapan

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