Polynomial calculus space and resolution width

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00518434" target="_blank" >RIV/67985840:_____/19:00518434 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/FOCS.2019.00081" target="_blank" >http://dx.doi.org/10.1109/FOCS.2019.00081</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/FOCS.2019.00081" target="_blank" >10.1109/FOCS.2019.00081</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial calculus space and resolution width

Popis výsledku v původním jazyce

We show that if a k-CNF requires width w to refute in resolution, then it requires space √w to refute in polynomial calculus, where the space of a polynomial calculus refutation is the number of monomials that must be kept in memory when working through the proof. This is the first analogue, in polynomial calculus, of Atserias and Dalmau’s result lower-bounding clause space in resolution by resolution width. As a by-product of our new approach to space lower bounds we give a simple proof of Bonacina’s recent result that total space in resolution (the total number of variable occurrences that must be kept in memory) is lower-bounded by the width squared. As corollaries of the main result we obtain some new lower bounds on the PCR space needed to refute specific formulas, as well as partial answers to some open problems about relations between space, size, and degree for polynomial calculus.

Název v anglickém jazyce

Polynomial calculus space and resolution width

Popis výsledku anglicky

We show that if a k-CNF requires width w to refute in resolution, then it requires space √w to refute in polynomial calculus, where the space of a polynomial calculus refutation is the number of monomials that must be kept in memory when working through the proof. This is the first analogue, in polynomial calculus, of Atserias and Dalmau’s result lower-bounding clause space in resolution by resolution width. As a by-product of our new approach to space lower bounds we give a simple proof of Bonacina’s recent result that total space in resolution (the total number of variable occurrences that must be kept in memory) is lower-bounded by the width squared. As corollaries of the main result we obtain some new lower bounds on the PCR space needed to refute specific formulas, as well as partial answers to some open problems about relations between space, size, and degree for polynomial calculus.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA19-05497S" target="_blank" >GA19-05497S: Složitost matematických důkazů a struktur</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

60th Annual Symposium on Foundations of Computer Science (FOCS)

ISBN

978-1-7281-4952-3

ISSN

0272-5428

e-ISSN

—

Počet stran výsledku

13

Strana od-do

1325-1337

Název nakladatele

IEEE

Místo vydání

Piscataway

Místo konání akce

Baltimore

Datum konání akce

9. 11. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000510015300072