Abstract

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.

BibTeX

@article{Multiset_Ordering_NPC-AFP,
  author  = {René Thiemann and Lukas Schmidinger},
  title   = {The Generalized Multiset Ordering is NP-Complete},
  journal = {Archive of Formal Proofs},
  month   = {April},
  year    = {2022},
  note    = {\url{https://isa-afp.org/entries/Multiset_Ordering_NPC.html},
            Formal proof development},
  ISSN    = {2150-914x},
}