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Computability Back

  • 探索一個問題的Computability主要從兩個方面討論

    • In Theory
      • 並不是所有的數學問題都是理論上可解決的.
      • 如果某问题理論上不能解決, 我們稱之為Undecidable (不可判定的)
    • In Practices
      • 在實際項目中, 倘若一個算法它的時間複雜度達到指數級別, 我們則之為Incomputable (不可計算的). (量子計算機或許是一個特例, 如果能實現指數級計算)
  • 問題的劃分

    • NP: 有多項式級別的判定算法
    • P: 有多項式級別的求解算法
    • EXP: 有指數式級別的求解算法
    • NP-Complete(NPC): 有多項式級別轉化成NP問題的算法(如果能有效地解決該類問題, 則所有NP都能有效解決)
      • 3-Color Problem
      • TSP
      • Circuit-SAT


  • Reduction is a general technique for showing that one problem is harder (easier) than another.
  • Reduction of NPC

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