伪随机性与组合结构
Pseudorandomness and Combinatorial Constructions
摘要：
在组合数学中，概率方法是一个非常强大的工具来证明组合对象的存在性，具有有趣和有用的性质。具有这种性质的对象的显式构造通常非常困难，或者是未知的。在计算机科学中，对于同一问题，概率算法有时比已知的确定性算法更简单和更有效。尽管有随机选择的力量的证据，伪随机性的计算理论表明，在某些复杂性理论的假设下，每一个概率算法都有一个有效的确定性模拟和大量的概率方法的应用可以转换为显式的结构。在这篇综述论文中，我们描述了伪随机性计算理论的条件"去随机化“结果和某些组合对象（如纠错码和"随机性提取器”）的无条件显式构造之间的联系。''
英文摘要：
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or unknown. In computer science, probabilistic algorithms are sometimes simpler and more efficient than the best known deterministic algorithms for the same problem. Despite this evidence for the power of random choices, the computational theory of pseudorandomness shows that, under certain complexity-theoretic assumptions, every probabilistic algorithm has an efficient deterministic simulation and a large class of applications of the the probabilistic method can be converted into explicit constructions. In this survey paper we describe connections between the conditional ``derandomization'' results of the computational theory of pseudorandomness and unconditional explicit constructions of certain combinatorial objects such as error-correcting codes and ``randomness extractors.''
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