Positive Moments Forever: Undecidable and Decidable Cases
Algebraic Geometry
2025-05-28 v2 Computational Complexity
Quantum Physics
Abstract
We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and undecidability for matrices over certain commutative and non-commutative polynomial rings. As consequences, we deduce that positivity is decidable for simple unitary linear recurrence sequences and undecidable for linear recurrence sequences over commutative polynomial rings. As a byproduct, we also prove a free version of Polya's theorem.
Cite
@article{arxiv.2404.15053,
title = {Positive Moments Forever: Undecidable and Decidable Cases},
author = {Gemma De les Coves and Joshua Graf and Andreas Klingler and Tim Netzer},
journal= {arXiv preprint arXiv:2404.15053},
year = {2025}
}
Comments
17 pages, v2: close to published version