The power of negative reasoning

0546771 - MÚ 2022 RIV DE eng C - Conference Paper (international conference)
de Rezende, Susanna F. - Lauria, M. - Nordström, J. - Sokolov, D.
The power of negative reasoning.
36th Computational Complexity Conference (CCC 2021). Dagstuhl: Schloss Dagstuhl, Leibniz-Zentrum für Informatik, 2021 - (Kabanets, V.), č. článku 40. Leibniz International Proceedings in Informatics, 200. ISBN 978-3-95977-193-1. ISSN 1868-8969.
[36th Computational Complexity Conference (CCC 2021). Toronto (CA), 20.07.2021-23.07.2021]
Institutional support: RVO:67985840
Keywords : proof complexity * polynomial calculus * nullstellensatz * sums-of-squares * Sherali-Adams
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://dx.doi.org/10.4230/LIPIcs.CCC.2021.40

Semialgebraic proof systems have been studied extensively in proof complexity since the late 1990s to understand the power of Gröbner basis computations, linear and semidefinite programming hierarchies, and other methods. Such proof systems are defined alternately with only the original variables of the problem and with special formal variables for positive and negative literals, but there seems to have been no study how these different definitions affect the power of the proof systems. We show for Nullstellensatz, polynomial calculus, Sherali-Adams, and sums-of-squares that adding formal variables for negative literals makes the proof systems exponentially stronger, with respect to the number of terms in the proofs. These separations are witnessed by CNF formulas that are easy for resolution, which establishes that polynomial calculus, Sherali-Adams, and sums-of-squares cannot efficiently simulate resolution without having access to variables for negative literals.
Permanent Link: http://hdl.handle.net/11104/0323158