Ordered and Unordered Tree Inclusion
SIAM Journal on Computing
Linear Higher-Order Matching Is NP-Complete
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
A Decidable Variant of Higher Order Matching
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Decidability of fourth-order matching
Mathematical Structures in Computer Science
Towards abstract categorial grammars
ACL '01 Proceedings of the 39th Annual Meeting on Association for Computational Linguistics
On the complexity of higher-order matching in the linear λ-calculus
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Syntactic descriptions: a type system for solving matching equations in the linear λ-calculus
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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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.