Títol | Bounded Second-Order Unification Is NP-Complete |
Publication Type | Conference Paper |
Year of Publication | 2006 |
Authors | Levy J [1], Schmidt-Schauss M [2], Villaret M [3] |
Conference Name | Lecture Notes in Computer Science |
Volume | 4098 |
Editor | Springer-Verlag |
Paginació | 400-414 |
Resum | Bounded Second-Order Unification is the problem of deciding, for a given second-order equation t=u and a positive integer m, whether there exists a unifier sigma 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. |