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对于复杂性理论的一点探讨 孙广中 [email_address]
计算理论与计算复杂性理论 对于计算的形式描述 可计算与不可计算 计算复杂性的刻画 计算复杂性理论的应用 新的计算模型    
算法的定义 为实现某个任务而构成的简单指令集 有穷的计算良过程 通过有限多次运算可以决定的过程 正确 直观,非形式
算法的定义 希尔伯特第十问题( 1900 ) 设计一个算法来判断多项式是否有整数根 算法:通过有限多次运算可以决定的过程 Alan  Turing & Alonzo Church ( 1936 ) 图灵机程序 算法:图灵机程序 形式化的,精确的
可计算与不可计算 停机问题 希尔伯特第十问题 软件验证
计算复杂性的刻画 P 类 ( Polynomial) NP 类 ( Nondeterministic Polynomial  ) PSPACE 类 IP 类 , RP 类 , … NP- 完全理论
计算复杂性理论的应用 算法分析 近似算法的下界 随机算法
新的计算模型 DNA 计算 量子计算 Richard Feynman  1982 David Deutsch  1985 A.C. Yao 1993 Peter Shor  1994 Grover L. K.  1996
复杂性理论 对于复杂的形式描述 可描述与不可描述 复杂性的刻画 复杂性理论的应用 新的模型
是否需要这方面的研究?
谢谢大家!

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