Skolem meets schanuel

Y Bilu, F Luca, J Nieuwveld, J Ouaknine… - arXiv preprint arXiv …, 2022 - arxiv.org
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 …

Does a program yield the right distribution? Verifying probabilistic programs via generating functions

M Chen, JP Katoen, L Klinkenberg… - … Conference on Computer …, 2022 - Springer
We study discrete probabilistic programs with potentially unbounded looping behaviors over
an infinite state space. We present, to the best of our knowledge, the first decidability result …

On the skolem problem and the skolem conjecture

R Lipton, F Luca, J Nieuwveld, J Ouaknine… - Proceedings of the 37th …, 2022 - dl.acm.org
It is a longstanding open problem whether there is an algorithm to decide the Skolem
Problem for linear recurrence sequences (LRS) over the integers, namely whether a given …

Equivalence and similarity refutation for probabilistic programs

K Chatterjee, EK Goharshady, P Novotný… - Proceedings of the ACM …, 2024 - dl.acm.org
We consider the problems of statically refuting equivalence and similarity of output
distributions defined by a pair of probabilistic programs. Equivalence and similarity are two …

Skolem Meets Bateman-Horn

F Luca, J Maynard, A Noubissie, J Ouaknine… - arXiv preprint arXiv …, 2023 - arxiv.org
The Skolem Problem asks to determine whether a given integer linear recurrence sequence
has a zero term. This problem arises across a wide range of topics in computer science …

Completing the picture for the Skolem Problem on order-4 linear recurrence sequences

P Bacik - arXiv preprint arXiv:2409.01221, 2024 - arxiv.org
For almost a century, the decidability of the Skolem Problem-that is, the problem of finding
whether a given linear recurrence sequence (LRS) has a zero term-has remained open. A …

Computing zeta functions of large polynomial systems over finite fields

Q Cheng, JM Rojas, D Wan - Journal of Complexity, 2022 - Elsevier
We improve the algorithms of Lauder-Wan [11] and Harvey [8] to compute the zeta function
of a system of m polynomial equations in n variables, over the q element finite field F q, for …