How to fit large complexity classes into TFNP
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916753499488256 |
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| author | Thapen, Neil |
| author_facet | Thapen, Neil |
| contents | Subclasses of TFNP (total functional NP) are usually defined by specifying a complete problem, which is necessarily in TFNP, and including all problems many-one reducible to it. We study two notions of how a TFNP problem can be reducible to an object, such as a complexity class, outside TFNP. This gives rise to subclasses of TFNP which capture some properties of that outside object. We show that well-known subclasses can arise in this way, for example PPA from reducibility to parity P and PLS from reducibility to P^NP.
We study subclasses arising from PSPACE and the polynomial hierarchy, and show that they are characterized by the propositional proof systems Frege and constant-depth Frege, extending the known pairings between natural TFNP subclasses and proof systems.
We study approximate counting from this point of view, and look for a subclass of TFNP that gives a natural home to combinatorial principles such as Ramsey which can be proved using approximate counting. We relate this to the recently-studied Long choice and Short choice problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to fit large complexity classes into TFNP Thapen, Neil Computational Complexity Logic in Computer Science Subclasses of TFNP (total functional NP) are usually defined by specifying a complete problem, which is necessarily in TFNP, and including all problems many-one reducible to it. We study two notions of how a TFNP problem can be reducible to an object, such as a complexity class, outside TFNP. This gives rise to subclasses of TFNP which capture some properties of that outside object. We show that well-known subclasses can arise in this way, for example PPA from reducibility to parity P and PLS from reducibility to P^NP. We study subclasses arising from PSPACE and the polynomial hierarchy, and show that they are characterized by the propositional proof systems Frege and constant-depth Frege, extending the known pairings between natural TFNP subclasses and proof systems. We study approximate counting from this point of view, and look for a subclass of TFNP that gives a natural home to combinatorial principles such as Ramsey which can be proved using approximate counting. We relate this to the recently-studied Long choice and Short choice problems. |
| title | How to fit large complexity classes into TFNP |
| topic | Computational Complexity Logic in Computer Science |
| url | https://arxiv.org/abs/2412.09984 |