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arXiv · 2404.15053

Positive Moments Forever: Undecidable and Decidable Cases

Gemma De les Coves·Joshua Graf·Andreas Klingler·Tim Netzer
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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.

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Gemma De les Coves, Joshua Graf, Andreas Klingler, Tim Netzer. 2024-04-23. Positive Moments Forever: Undecidable and Decidable Cases. https://doi.org/10.1016/j.laa.2025.05.015

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