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Electronic Colloquium on Computational Complexity

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Reports tagged with Extremal Combinatorics:
TR97-012 | 19th March 1997
Luca Trevisan

On Local versus Global Satisfiability

We prove an extremal combinatorial result regarding
the fraction of satisfiable clauses in boolean CNF
formulae enjoying a locally checkable property, thus
solving a problem that has been open for several years.

We then generalize the problem to arbitrary constraint
satisfaction ... more >>>

TR19-013 | 31st January 2019
Joshua Brakensiek, Sivakanth Gopi, Venkatesan Guruswami

CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial Representations

We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo $M$, for various choices of the modulus $M$. Due to the known classification of tractable Boolean CSPs, this mainly reduces to the study of three cases: 2SAT, HornSAT, ... more >>>

TR22-037 | 10th March 2022
Abhibhav Garg, Rafael Mendes de Oliveira, Akash Sengupta

Robust Radical Sylvester-Gallai Theorem for Quadratics

We prove a robust generalization of a Sylvester-Gallai type theorem for quadratic polynomials, generalizing the result in [S'20].
More precisely, given a parameter $0 < \delta \leq 1$ and a finite collection $\mathcal{F}$ of irreducible and pairwise independent polynomials of degree at most 2, we say that $\mathcal{F}$ is a ... more >>>

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