In this article we survey recent progress in the algorithmic theory of matrix semigroups. The
main objective in this area of study is to construct algorithms that decide various properties …

We study both the Submonoid Membership problem and the Rational Subset Membership
problem in finitely generated nilpotent groups. We give two reductions with important …

The submonoid membership problem for a finitely generated group $ G $ is the decision
problem, where for a given finitely generated submonoid $ M $ of $ G $ and a group element …

We prove the following results:(1) There is a one-relator inverse monoid Inv ⟨ A\,|\, w= 1 ⟩
Inv⟨ A| w= 1⟩ with undecidable word problem; and (2) There are one-relator groups with …

We consider the rational subset membership problem for Baumslag-Solitar groups. These
groups form a prominent class in the area of algorithmic group theory, and they were …

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We study the computational complexity of existential Presburger arithmetic with (possibly
nested occurrences of) a Kleene-star operator. In addition to being a natural extension of …

The goal of this book is to showcase new directions in group theory motivated by com-puter
science. The subtitle (GAGTA book) reflects the fact that the book follows the course of the …

The classic knapsack and related problems have natural generalizations to arbitrary (non-
commutative) groups, collectively called knapsack-type problems in groups. We study the …

Motivated by approaches to the word problem for one-relation monoids arising from work of
Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis, and Meakin (2001), we …