113 citations · 260 across the 57 of their papers we have counts for
16 papers · 1 filter
On the Complexity of the Skolem Problem at Low Orders
Piotr Bacik, Joël Ouaknine, James Worrell
The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) over the integers has a zero term, that is, whether there e…
On the Counting Complexity of the Skolem Problem
Gorav Jindal, Joël Ouaknine
The Skolem Problem asks, given an integer linear recurrence sequence (LRS), to determine whether the sequence contains a zero term or not. Its decidability is a longstanding open p…
Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set
Julian D'Costa, Engel Lefaucheux, Eike Neumann +2
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for…
On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets
Julian D'Costa, Engel Lefaucheux, Eike Neumann +2
We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for…
Reachability in Dynamical Systems with Rounding
Christel Baier, Florian Funke, Simon Jantsch +6
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a…
On Reachability Problems for Low-Dimensional Matrix Semigroups
Thomas Colcombet, Joël Ouaknine, Pavel Semukhin +1
We consider the Membership and the Half-Space Reachability problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for…
The Semialgebraic Orbit Problem
Shaull Almagor, Joël Oukanine, James Worrell
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurr…
Effective Divergence Analysis for Linear Recurrence Sequences
Shaull Almagor, Brynmor Chapman, Mehran Hosseini +2
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomia…
O-Minimal Invariants for Discrete-Time Dynamical Systems
Shaull Almagor, Dmitry Chistikov, Joël Ouaknine +1
Termination analysis of linear loops plays a key rôle in several areas of computer science, including program verification and abstract interpretation. Already for the simplest var…
Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem
Nathanaël Fijalkow, Pierre Ohlmann, Joël Ouaknine +2
The \emph{Orbit Problem} consists of determining, given a linear transformation on , together with vectors and , whether the orbit of under repeated ap…
The Polytope-Collision Problem
Shaull Almagor, Joël Ouaknine, James Worrell
The Orbit Problem consists of determining, given a matrix and vectors , whether there exists such that .…
On the Polytope Escape Problem for Continuous Linear Dynamical Systems
Joël Ouaknine, João Sousa-Pinto, James Worrell
The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function and a convex pol…
On Termination of Integer Linear Loops
Joël Ouaknine, João Sousa Pinto, James Worrell
A fundamental problem in program verification concerns the termination of simple linear loops of the form x := u ; while Bx >= b do {x := Ax + a} where x is a vector of variables,…
The Polyhedron-Hitting Problem
Ventsislav Chonev, Joël Ouaknine, James Worrell
We consider polyhedral versions of Kannan and Lipton's Orbit Problem (STOC '80 and JACM '86)---determining whether a target polyhedron V may be reached from a starting point x unde…
Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences
Joel Ouaknine, James Worrell
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)…
On the Complexity of the Orbit Problem
Ventsislav Chonev, Joël Ouaknine, James Worrell
We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem---determining whether a target vector space V may be reached from a starting point x under repeated app…