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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Yoshinaka, R. (2005). Higher-order matching in the linear lambda calculus in the absence of constants is NP-complete. In Lecture Notes in Computer Science (Vol. 3467, pp. 235–249). Springer Verlag. https://doi.org/10.1007/978-3-540-32033-3_18
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