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EXCICO

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Extremal Combinatorics and Circuit Complexity

Computational complexity theory is the systematic study of computational problems in order to classify them in terms of their inherent logical hardness. Several decades of research have not only given rise to important understand... ver más

01/01/2026

CAS

180K€

Presupuesto del proyecto: 180K€

Líder del proyecto

MATEMATICKY USTAV AV CR V.V.I. No se ha especificado una descripción o un objeto social para esta compañía.

Ver 3 Participantes

Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-05-15

HORIZON-MSCA-2022-PF-01-01: MSCA Postdoctoral Fellowships 2022 ExpectedOutcome:

I+D

Cerrada hace 2 años

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3 Participantes

CAS

180.42K€ | Lider

THE REGENTS OF THE UNIVERSIT...

LOS ANGELES UCLA SANTA BARBA...

N.D. | Participante

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Duración del proyecto: 31 meses Fecha Inicio: 2023-05-15
Fecha Fin: 2026-01-01

Líder del proyecto

MATEMATICKY USTAV AV CR V.V.I. No se ha especificado una descripción o un objeto social para esta compañía.

Presupuesto del proyecto 180K€

Descripción del proyecto Computational complexity theory is the systematic study of computational problems in order to classify them in terms of their inherent logical hardness. Several decades of research have not only given rise to important understanding of limits of computation, but have also developed algorithms which constitute a crucial part of modern life. A formidable challenge in complexity theory is to show non-linear lower bounds for an explicit Boolean function. Our project is motivated by this fundamental problem and in fact we will approach several such questions motivated by understanding the complexity of explicit Boolean functions. Our main objective look at circuit complexity through the lens of extremal combinatorics, a rich and vibrant of branch of combinatorics which studies objects satisfying various constraints. Therefore we aim to develop a systematic methodology which adopts tools of extremal combinatorics to tackle complexity problems. More concretely we attack the problem of lower bounds for depth-3 circuits and specifically attempt to prove sharp lower bounds for the Majority function thus breaking a barrier in this area. We will further extend the techniques used in recent breakthrough on the Sunflower Conjecture and apply it to CNF formula and the structure of their satisfying assignments. We will our new insights on the structure of satisfying assignments to develop new improved algorithms for the satisfiability problem (SAT).

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