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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On hardness of multilinearization, and VNP-completeness in characteristics 2
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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