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math.NT2026
Twisted Rational Zeros and Local-Global Principles for Linear Recurrence Sequences
Piotr Bacik
The Skolem Problem asks whether a given linear recurrence sequence (LRS) has a zero term, and is equivalent to proving an effective version of the Skolem-Mahler-Lech theorem, which…
cs.LO2026
On Variable-Bounded Non-Linear Expansions of Presburger Arithmetic
Piotr Bacik, Joris Nieuwveld, Joël Ouaknine +3
We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers…
cs.DM2026
On the Subspace Orbit Problem and the Simultaneous Skolem Problem
Piotr Bacik, Anton Varonka
The Orbit Problem asks whether the orbit of a point under a matrix reaches a given target set. When the target is a single point, the problem was shown to be decidable in polynomia…