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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 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…