The algebraic theory of automata was created by Schützenberger and Chomsky over 50
years ago and there has since been a great deal of development. Classical work on the …

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 …

This book presents the state-of-the-art results concerning recurrent sequences and their
practical applications in algebra, number theory, geometry of the complex plane, discrete …

Linear recurrence sequences permeate a vast number of areas of mathematics and
computer science. In this paper, we survey the state of the art concerning certain …

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks
whether all terms of the sequence are positive. We show that, for simple LRS (those whose …

We consider the decidability and complexity of the Ultimate Positivity Problem, which asks
whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are …

A sequence of real numbers is said to be positive if all terms are positive, and ultimately
positive if all but finitely many terms are positive. In this article we survey recent progress on …

We consider the MSO model-checking problem for simple linear loops, or equivalently
discrete-time linear dynamical systems, with semialgebraic predicates (ie, Boolean …

The Positivity Problem for linear recurrence sequences over a ring R of real algebraic
numbers is to determine, given an LRS \left(u_n\right)_n∈N over R, whether un≥ 0 for all n …

In the buyback problem, an algorithm observes a sequence of bids and must decide whether
to accept each bid at the moment it arrives, subject to some constraints on the set of …