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 consider two decision problems for linear recurrence sequences (LRS) over the
integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the …

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that
hold at each location of a given affine program (ie, a program having only non-deterministic …

Quantum computing combines quantum physics and computer science, by studying
computational models based on quantum physics (which is substantially di erent from …

We study the following decision problem: is the language recognized by a quantum finite
automaton empty or nonempty? We prove that this problem is decidable or undecidable …

A polynomial program is one in which all assignments are given by polynomial expressions
and in which all branching is nondeterministic (as opposed to conditional). Given such a …

We consider semigroup algorithmic problems in finitely generated metabelian groups. Our
paper focuses on three decision problems introduced by Choffrut and Karhum'aki (2005) …

The (left) linear hull of a weighted automaton over a field is a topological invariant. If the
automaton is minimal, the linear hull can be used to determine whether or not the automaton …

Let G be a unitriangular matrix group of nilpotency class at most ten. We show that the
Identity Problem (does a semigroup contain the identity matrix?) and the Group Problem (is …

Designed as a self-contained account of a number of key algorithmic problems and their
solutions for linear algebraic groups, this book combines in one single text both an …