Knapsack Problems for Wreath Products
Group Theory
2017-10-03 v2 Formal Languages and Automata Theory
Abstract
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group , knapsack (as well as the related subset sum problem) for the wreath product is NP-complete.
Cite
@article{arxiv.1709.09598,
title = {Knapsack Problems for Wreath Products},
author = {Moses Ganardi and Daniel König and Markus Lohrey and Georg Zetzsche},
journal= {arXiv preprint arXiv:1709.09598},
year = {2017}
}