Abstract
Bounded Second-Order Unification is the problem of deciding, for a given second-order equation \({t {\stackrel{_?}=} u}\) and a positive integer m, whether there exists a unifier σ such that, for every second-order variable F, the terms instantiated for F have at most m occurrences of every bound variable.
It is already known that Bounded Second-Order Unification is decidable and NP-hard, whereas general Second-Order Unification is undecidable. We prove that Bounded Second-Order Unification is NP-complete, provided that m is given in unary encoding, by proving that a size-minimal solution can be represented in polynomial space, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time.
This research has been partially founded by the CICYT research projects iDEAS (TIN2004-04343) and Mulog (TIN2004-07933-C03-01).
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Levy, J., Schmidt-Schauß, M., Villaret, M. (2006). Bounded Second-Order Unification Is NP-Complete. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_30
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DOI: https://doi.org/10.1007/11805618_30
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