On hardness of multilinearization, and VNP-completeness in characteristics 2

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00469668" target="_blank" >RIV/67985840:_____/16:00469668 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1145/2940323" target="_blank" >http://dx.doi.org/10.1145/2940323</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/2940323" target="_blank" >10.1145/2940323</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On hardness of multilinearization, and VNP-completeness in characteristics 2

Popis výsledku v původním jazyce

For a Boolean function f: {0, 1}n ... {0, 1}, let &fcirc; be the unique multilinear polynomial such that f(x) = &fcirc;(x) holds for every x in {0, 1}n. We show that, assuming VP ... VNP, there exists a polynomial-time computable f such that &fcirc; requires superpolynomial arithmetic circuits. In fact, this f can be taken as a monotone 2-CNF, or a product of affine functions. This holds over any field. To prove the results in characteristic 2, we design new VNP-complete families in this characteristic. This includes the polynomial ECn counting edge covers in a graph and the polynomial mcliquen counting cliques in a graph with deleted perfect matching. They both correspond to polynomial-time decidable problems, a phenomenon previously encountered only in characteristic ... 2.

Název v anglickém jazyce

On hardness of multilinearization, and VNP-completeness in characteristics 2

Popis výsledku anglicky

For a Boolean function f: {0, 1}n ... {0, 1}, let &fcirc; be the unique multilinear polynomial such that f(x) = &fcirc;(x) holds for every x in {0, 1}n. We show that, assuming VP ... VNP, there exists a polynomial-time computable f such that &fcirc; requires superpolynomial arithmetic circuits. In fact, this f can be taken as a monotone 2-CNF, or a product of affine functions. This holds over any field. To prove the results in characteristic 2, we design new VNP-complete families in this characteristic. This includes the polynomial ECn counting edge covers in a graph and the polynomial mcliquen counting cliques in a graph with deleted perfect matching. They both correspond to polynomial-time decidable problems, a phenomenon previously encountered only in characteristic ... 2.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

ACM Transactions on Computation Theory

ISSN

1942-3454

e-ISSN

—

Svazek periodika

9

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

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Kód UT WoS článku

000392673500001

EID výsledku v databázi Scopus

2-s2.0-85009085885