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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.15053 |
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| _version_ | 1866915306436296704 |
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| author | Coves, Gemma De les Graf, Joshua Klingler, Andreas Netzer, Tim |
| author_facet | Coves, Gemma De les Graf, Joshua Klingler, Andreas Netzer, Tim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive Moments Forever: Undecidable and Decidable Cases Coves, Gemma De les Graf, Joshua Klingler, Andreas Netzer, Tim Algebraic Geometry Computational Complexity Quantum Physics 13P99 (Primary), 11B37 (Secondary) 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. |
| title | Positive Moments Forever: Undecidable and Decidable Cases |
| topic | Algebraic Geometry Computational Complexity Quantum Physics 13P99 (Primary), 11B37 (Secondary) |
| url | https://arxiv.org/abs/2404.15053 |