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关于复杂性理论的一点探讨
孙广中
sungz@mail.ustc.edu.cn
计算理论与计算复杂性理论
• 关于计算的形式描述
• 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
演算−λ
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
• 关于复杂的形式描述
• 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?
大家谢谢
!

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