26 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Two Source Extractors for Asymptotically Optimal Entropy, and (Many) More

    Full text link
    A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications. These connections essentially show that an asymptotically optimal construction of one central object will lead to asymptotically optimal solutions to all the others. However, despite considerable effort, previous works can get close but still lack one final step to achieve truly asymptotically optimal constructions. In this paper we provide the last missing link, thus simultaneously achieving explicit, asymptotically optimal constructions and solutions for various well studied extractors and applications, that have been the subjects of long lines of research. Our results include: Asymptotically optimal seeded non-malleable extractors, which in turn give two source extractors for asymptotically optimal min-entropy of O(logn)O(\log n), explicit constructions of KK-Ramsey graphs on NN vertices with K=logO(1)NK=\log^{O(1)} N, and truly optimal privacy amplification protocols with an active adversary. Two source non-malleable extractors and affine non-malleable extractors for some linear min-entropy with exponentially small error, which in turn give the first explicit construction of non-malleable codes against 22-split state tampering and affine tampering with constant rate and \emph{exponentially} small error. Explicit extractors for affine sources, sumset sources, interleaved sources, and small space sources that achieve asymptotically optimal min-entropy of O(logn)O(\log n) or 2s+O(logn)2s+O(\log n) (for space ss sources). An explicit function that requires strongly linear read once branching programs of size 2nO(logn)2^{n-O(\log n)}, which is optimal up to the constant in O()O(\cdot). Previously, even for standard read once branching programs, the best known size lower bound for an explicit function is 2nO(log2n)2^{n-O(\log^2 n)}.Comment: Fixed some minor error

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 244, ESA 2022, Complete Volume

    Get PDF
    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Proceedings of the European Conference on Agricultural Engineering AgEng2021

    Get PDF
    This proceedings book results from the AgEng2021 Agricultural Engineering Conference under auspices of the European Society of Agricultural Engineers, held in an online format based on the University of Évora, Portugal, from 4 to 8 July 2021. This book contains the full papers of a selection of abstracts that were the base for the oral presentations and posters presented at the conference. Presentations were distributed in eleven thematic areas: Artificial Intelligence, data processing and management; Automation, robotics and sensor technology; Circular Economy; Education and Rural development; Energy and bioenergy; Integrated and sustainable Farming systems; New application technologies and mechanisation; Post-harvest technologies; Smart farming / Precision agriculture; Soil, land and water engineering; Sustainable production in Farm buildings

    Shadows of Newton Polytopes

    Get PDF
    We define the shadow complexity of a polytope P as the maximum number of vertices in a linear projection of P to the plane. We describe connections to algebraic complexity and to parametrized optimization. We also provide several basic examples and constructions, and develop tools for bounding shadow complexity

    Preface

    Get PDF

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

    Get PDF

    29th International Symposium on Algorithms and Computation: ISAAC 2018, December 16-19, 2018, Jiaoxi, Yilan, Taiwan

    Get PDF
    corecore