Speaker
Description
Ruiwen Dong
Best Student Paper Track B
Abstract: We consider semigroup algorithmic problems in the wreath product $\mathbb{Z} \wr \mathbb{Z}$.
Our paper focuses on two decision problems introduced by Choffrut and Karhum\"{a}ki (2005): the \emph{Identity Problem} (does a semigroup contain the neutral element?) and the \emph{Group Problem} (is a semigroup a group?) for finitely generated sub-semigroups of $\mathbb{Z} \wr \mathbb{Z}$.
We show that both problems are decidable.
Our result complements the undecidability of the \emph{Semigroup Membership Problem} (does a semigroup contain a given element?) in $\mathbb{Z} \wr \mathbb{Z}$ shown by Lohrey, Steinberg and Zetzsche (ICALP 2013), and contributes an important step towards solving semigroup algorithmic problems in general metabelian groups.