The Power of Negative Reasoning
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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.
Original language | English |
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Title of host publication | 36th Computational Complexity Conference, CCC 2021 |
Editors | Valentine Kabanets |
Number of pages | 24 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publication date | 2021 |
Article number | 40 |
ISBN (Electronic) | 978-3-95977-193-1 |
DOIs | |
Publication status | Published - 2021 |
Event | 36th Computational Complexity Conference, CCC 2021 - Virtual, Toronto, Canada Duration: 20 Jul 2021 → 23 Jul 2021 |
Conference
Conference | 36th Computational Complexity Conference, CCC 2021 |
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Land | Canada |
By | Virtual, Toronto |
Periode | 20/07/2021 → 23/07/2021 |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 200 |
ISSN | 1868-8969 |
Bibliographical note
Publisher Copyright:
© Susanna F. de Rezende, Massimo Lauria, Jakob Nordström, and Dmitry Sokolov;
- Nullstellensatz, Polynomial calculus, Proof complexity, Sherali-Adams, Sums-of-squares
Research areas
ID: 306898812