Strength and limitations of Sherali-Adams and Nullstellensatz proof systems
Year: 2024
Type: article
Abstract: 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.
Source: Annals of Pure and Applied Logic
Authors: Ilario Bonacina, Maria Luisa Bonet
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,420
Awards: G1175115578, G121809054, G1855990336, G2262748287, G2309174360, G2660406951, G279363373, G300979063, G34346518, G3480869486, G3518538256, G3690828678, G425668148, G430777504, G4526231891, G5080475149, G5284880062, G5421974903, G6891804154, G7084143925, G7386763261, G8684520763, G897484643, G99296377
OpenAlex ID: W4404815165