Project description
Advancing computational complexity theory through extremal combinatorics
Computational complexity theory classifies computational problems based on their inherent logical hardness. Funded by the Marie Skłodowska-Curie Actions programme, the EXCICO project will address a significant challenge in computational complexity theory: imposing nonlinear lower bounds for explicit Boolean functions. By viewing circuit complexity through the lens of extremal combinatorics – a branch of combinatorics studying objects under various constraints – EXCICO hopes to develop a systematic methodology for tackling complexity problems. Specifically, the research will focus on lower bounds for depth-3 circuits, aiming to prove sharp lower bounds for the Majority function. The team also plans to extend techniques from the recent breakthrough on the sunflower conjecture, applying them to conjunctive normal form formulas and their satisfying assignments.
Objective
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).
Programme(s)
- HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA) Main Programme
Funding Scheme
HORIZON-TMA-MSCA-PF-GF - HORIZON TMA MSCA Postdoctoral Fellowships - Global FellowshipsCoordinator
115 67 Praha
Czechia