The power of negative reasoning

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546771" target="_blank" >RIV/67985840:_____/21:00546771 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2021.40" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.CCC.2021.40</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2021.40" target="_blank" >10.4230/LIPIcs.CCC.2021.40</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The power of negative reasoning

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The power of negative reasoning

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

36th Computational Complexity Conference (CCC 2021)

ISBN

978-3-95977-193-1

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

24

Strana od-do

40

Název nakladatele

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl

Místo konání akce

Toronto

Datum konání akce

20. 7. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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