Theory of computing

Regular Expressions/DFA/NFA

Regular Expressions (RE) 正規式
它的規則:
https://www.runoob.com/regexp/regexp-metachar.html
(測試網站):
https://tool.oschina.net/regex/

Finite State Machine:(有限狀態機)
Finite Automaton:(有窮自動機)
DFA/NFA:確定的又窮自動機/非確定的有窮自動機
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Two ways to define a set of strings (language)

Regular expressions (REs)
Deterministic finite automatia (DFAs)

conclusion:

  1. Remarkable fact. DFAs and REs are equivalent (等價)
  2. In short, there is no formal language that can be recognized by some NFA and not by any DFA
  3. NFAs and REs are equivalent
  4. Not all formal languages are regular

Turing Machines

DFAs 與 TMs的比較
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Universality

All computational devices are equivalent
Turing as a definition of what we can compute
Q&A : 圖靈機,Java,mobile phone,are universality

Computability

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根據前面的理論如果問題不能計算那麼所有的計算機都不能計算因爲
All computational devices are equivalent
The halting problem is undecidable: (圖靈機停機問題)https://zhidao.baidu.com/question/22004860.html

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