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  • 标题:The Space Complexity of Samplin
  • 本地全文:下载
  • 作者:Eshan Chattopadhyay ; Jesse Goodman ; David Zuckerman
  • 期刊名称:Electronic Colloquium on Computational Complexity
  • 印刷版ISSN:1433-8092
  • 出版年度:2021
  • 卷号:21
  • 语种:English
  • 出版社:Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
  • 摘要:Recently, there has been exciting progress in understanding the complexity of distributions. Here, the goal is to quantify the resources required to generate (or sample) a distribution. Proving lower bounds in this new setting is more challenging than in the classical setting, and has yielded interesting new techniques and surprising applications. In this work, we initiate a study of the complexity of sampling with limited memory, and obtain the first nontrivial sampling lower bounds against oblivious read-once branching programs (ROBPs). In our first main result, we show that any distribution sampled by an ROBP of width 2(n) has statistical distance 1−2−(n) from any distribution that is uniform over a good code. More generally, we obtain sampling lower bounds for any list decodable code, which are nearly tight. Previously, such a result was only known for sampling in AC0 (Lovett and Viola, CCC'11; Beck, Impagliazzo and Lovett, FOCS'12). As an application of our result, a known connection implies new data structure lower bounds for storing codewords. In our second main result, we prove a direct product theorem for sampling with ROBPs. Previously, no direct product theorems were known for the task of sampling, for any computational model. A key ingredient in our proof is a simple new lemma about amplifying statistical distance between sequences of somewhat-dependent random variables. Using this lemma, we also obtain a simple new proof of a known lower bound for sampling disjoint sets using two-party communication protocols (Göös and Watson, RANDOM'19).
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