Real Stability and Log Concavity are coNP-Hard
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916255038963712 |
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| author | Chin, Tracy |
| author_facet | Chin, Tracy |
| contents | Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real stable or log concave are coNP-hard. On the other hand, while all homogeneous real-stable polynomials are Lorentzian and all Lorentzian polynomials are log concave on the positive orthant, the problem of deciding whether a polynomial of fixed degree is Lorentzian can be solved in polynomial time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real Stability and Log Concavity are coNP-Hard Chin, Tracy Optimization and Control Computational Complexity Combinatorics Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real stable or log concave are coNP-hard. On the other hand, while all homogeneous real-stable polynomials are Lorentzian and all Lorentzian polynomials are log concave on the positive orthant, the problem of deciding whether a polynomial of fixed degree is Lorentzian can be solved in polynomial time. |
| title | Real Stability and Log Concavity are coNP-Hard |
| topic | Optimization and Control Computational Complexity Combinatorics |
| url | https://arxiv.org/abs/2405.00162 |