Ultimate Polynomial Time
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
1999
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| _version_ | 1866918162969133056 |
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| author | Malajovich, Gregorio |
| author_facet | Malajovich, Gregorio |
| contents | The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$.
The $τ$-Conjecture for polynomials implies that $\mathcal{UP}$ does not contain the class of non-deterministic polynomial time problems definable without constants over $\mathbb C$.
This latest statement implies that $\mathcal P \ne \mathcal{NP}$ over $\mathbb C$.
A notion of `ultimate complexity' of a problem is suggested. It provides lower bounds for the complexity of structured problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9904130 |
| institution | arXiv |
| publishDate | 1999 |
| record_format | arxiv |
| spellingShingle | Ultimate Polynomial Time Malajovich, Gregorio Numerical Analysis The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $τ$-Conjecture for polynomials implies that $\mathcal{UP}$ does not contain the class of non-deterministic polynomial time problems definable without constants over $\mathbb C$. This latest statement implies that $\mathcal P \ne \mathcal{NP}$ over $\mathbb C$. A notion of `ultimate complexity' of a problem is suggested. It provides lower bounds for the complexity of structured problems. |
| title | Ultimate Polynomial Time |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/9904130 |