Regular Languages

• Regular expressions
• Re语言
• Equivalence between languages accepted by FA and regular languages
• Closure Properties

Re喉部的表达式

Regular expression over alphabet Σ

• -- regular expression.
• ε-- regular expression.
• F或任何aσ∈, a is a ordinary expression.
• IF R1和R2是正则表达式，然后

-(r1 + r2) is an ordinary expression.

-(r1×r2) is an ordinary expression.

-(r1* ) is an ordinary expression.

• AnythingeLSE不是正则表达式。

• is a regular language equivalent to the regular expression.
• {ε} is a regular language equivalent to the regular expressione.
• F或任何符号aσ∈, {a} is a regular language equivalent to the regular expression a.
• IF L1和L2是等于正则表达式R1和R2的普通语言，然后

-are regular languages equivalent to (r1 + r2), (r1×r2）和（R1*）。

Simple examples

Letσ= {0,1}。

• {σ∈A*|adoes not contain 1's}

-(0*)

• {σ∈A*|acOntains 1仅

-(1×(1*)) (which can can be denoted by (1+))

• σ*

-（（0+1）*）

• {σ∈A*|acOntains仅0或仅1}

-((00*)+(11*))

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