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On the -adic Skolem Problem
Piotr Bacik, Joël Ouaknine, David Purser +1
The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) has a zero term. Showing decidability of this problem is equivalent to giving an effective pro…
Skolem Meets Schanuel
Yuri Bilu, Florian Luca, Joris Nieuwveld +3
The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a linear recurrence sequence is the union of a finite set and finitely many arithmetic progressions. The c…
Porous Invariants
Engel Lefaucheux, Joël Ouaknine, David Purser +1
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in f…
The Orbit Problem for Parametric Linear Dynamical Systems
Christel Baier, Florian Funke, Simon Jantsch +7
We study a parametric version of the Kannan-Lipton Orbit Problem for linear dynamical systems. We show decidability in the case of one parameter and Skolem-hardness with two or mor…