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Trade-offs between size and degree in polynomial calculus
KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.ORCID iD: 0000-0002-2700-4285
KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.
2020 (English)In: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2020Conference paper, Published paper (Refereed)
Abstract [en]

Building on [Clegg et al.’96], [Impagliazzo et al.’99] established that if an unsatisfiable k-CNF formula over n variables has a refutation of size S in the polynomial calculus resolution proof system, then this formula also has a refutation of degree k + O(n log S). The proof of this works by converting a small-size refutation into a small-degree one, but at the expense of increasing the proof size exponentially. This raises the question of whether it is possible to achieve both small size and small degree in the same refutation, or whether the exponential blow-up is inherent. Using and extending ideas from [Thapen’16], who studied the analogous question for the resolution proof system, we prove that a strong size-degree trade-off is necessary.

Place, publisher, year, edition, pages
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2020.
Series
Leibniz International Proceedings in Informatics, ISSN 1868-8969 ; 151
Keywords [en]
Colored polynomial local search, PCR, Polynomial calculus, Polynomial calculus resolution, Proof complexity, Resolution, Size-degree trade-off, Economic and social effects, Optical resolving power, Polynomials, Blow-up, K-CNF formulas, Local search, Resolution proofs, Trade off, Calculations
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-267991DOI: 10.4230/LIPIcs.ITCS.2020.72Scopus ID: 2-s2.0-85078035428ISBN: 9783959771344 (print)OAI: oai:DiVA.org:kth-267991DiVA, id: diva2:1416174
Conference
11th Innovations in Theoretical Computer Science Conference, ITCS 2020, January 12-14, 2020, Seattle, Washington, USA.
Note

QC 20200322

Available from: 2020-03-22 Created: 2020-03-22 Last updated: 2020-03-22Bibliographically approved

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Nordström, JakobSwernofsky, Jospeh Alexander

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