Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for...Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.展开更多
We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability o...We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to average-case reductions; pseudorandomness and extractor constructions; and Valiant＇s new theory of holographic algorithms and reductions.展开更多
文摘Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.
文摘We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to average-case reductions; pseudorandomness and extractor constructions; and Valiant＇s new theory of holographic algorithms and reductions.
