Notation

Let r be the regular expression.

The regular language corresponding to regular expression r cam ne denoted by L(r).

Some rules for language operations

Let r, s and t be the languages over {0,1}

Rewrite rules for regular expressions

Let r, s and t be the regular expressions over {0,1}.

Some more notations

Let ∑= {0,1}.

• Parentheses in the regular expressions can be removes when the order of evaluation is clear.

-   ((0+1)*) ≠ 0+1*

-   ((0*)+(1*)) = 0* + 1*

• For concatenation, ×can be omitted.
• r× r× r... r can be denoted by rn.

Let ∑= {0,1}.

• { ∑∈α*| α contains odd number of 1's}

-    0*(10*10*)*10*

• { ∑∈ α *| any two 0's in aare separated by three 1's}

-    1*(0111)*01* + 1*

• { ∑∈α*| α is a binary number divisible by 4}

-    (0+1)*00

• { ∑∈α*| α does not contain 11}

-    0*(10+)* (1+ε) or (0+10)* (1+ε)

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