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Displaying similar documents to “Exact Expectation and Variance of Minimal Basis of Random Matroids”

Random matroids

Kordecki Wojciech

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CONTENTS1. Introduction.............................................................................52. Matroids..................................................................................6  2.1. Notations and basic properties...........................................6  2.2. Gaussian coefficients.......................................................10  2.3. Projective geometries.......................................................11  2.4. Special classes................................................................143....

Smooth and sharp thresholds for random k -XOR-CNF satisfiability

Nadia Creignou, Hervé Daudé (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The aim of this paper is to study the threshold behavior for the satisfiability property of a random k -XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with k variables per equation. For k 3 we show the existence of a sharp threshold for the satisfiability of a random k -XOR-CNF formula, whereas there are smooth thresholds for k = 1 and k = 2 .