Strength and limitations of Sherali-Adams and Nullstellensatz proof systems
We compare the strength of the algebraic proof systems Sherali-Adams (SA) and Nullstellensatz (NS) with Frege-style proof systems. Unlike bounded-depth Frege, SA has polynomial-size proofs of the pigeonhole principle (PHP). A natural question is whether adding PHP to bounded-depth Frege is enough to...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/421056 |
| Acceso en línea: | https://hdl.handle.net/2117/421056 https://dx.doi.org/10.1016/j.apal.2024.103538 |
| Access Level: | acceso abierto |
| Palabra clave: | Bounded-depth Frege Nullstellensatz Sherali-Adams Pigeonhole principle Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Sumario: | We compare the strength of the algebraic proof systems Sherali-Adams (SA) and Nullstellensatz (NS) with Frege-style proof systems. Unlike bounded-depth Frege, SA has polynomial-size proofs of the pigeonhole principle (PHP). A natural question is whether adding PHP to bounded-depth Frege is enough to simulate SA. We show that SA, with unary integer coefficients, lies strictly between tree-like depth-1 Frege + PHP and tree-like Resolution. We introduce a levelled version of PHP (L PHP) and we show that SA with integer coefficients lies strictly between tree-like depth-1 Frege + L PHP and Resolution. Analogous results are shown for NS using the bijective (i.e. onto and functional) pigeonhole principle and a leveled version of it. |
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