On subset sum problem in branch groups

TL;DR

This paper proves that the subset sum problem is NP-complete in the first Grigorchuk group and NP-hard in a broader class of branch groups, highlighting computational complexity in group theory.

Contribution

It establishes NP-completeness of the subset sum problem in the first Grigorchuk group and NP-hardness in weakly regular branch groups, extending complexity results to new algebraic structures.

Findings

NP-complete in the first Grigorchuk group

NP-hard in weakly regular branch groups

NP-complete if the group is contracting

Abstract

We consider a group-theoretic analogue of the classic subset sum problem. In this brief note, we show that the subset sum problem is NP-complete in the first Grigorchuk group. More generally, we show NP-hardness of that problem in weakly regular branch groups, which implies NP-completeness if the group is, in addition, contracting.