The Generalized Multiset Ordering is NP-Complete

René Thiemann 🌐 and Lukas Schmidinger

April 20, 2022

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We consider the problem of comparing two multisets via the generalized multiset ordering. We show that the corresponding decision problem is NP-complete. To be more precise, we encode multiset-comparisons into propositional formulas or into conjunctive normal forms of quadratic size; we further prove that satisfiability of conjunctive normal forms can be encoded as multiset-comparison problems of linear size. As a corollary, we also show that the problem of deciding whether two terms are related by a recursive path order is NP-hard, provided the recursive path order is based on the generalized multiset ordering.


BSD License


Session Multiset_Ordering_NPC