Knapsack in graph groups, HNN-extensions and amalgamated products
Group Theory
2015-09-22 v1 Formal Languages and Automata Theory
Abstract
It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of the knapsack problem is passed on to finite extensions, HNN-extensions over finite associated subgroups, and amalgamated products with finite identified subgroups.
Cite
@article{arxiv.1509.05957,
title = {Knapsack in graph groups, HNN-extensions and amalgamated products},
author = {Markus Lohrey and Georg Zetzsche},
journal= {arXiv preprint arXiv:1509.05957},
year = {2015}
}
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42 pages