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# Regular Expression s

Regular Expression s Are Used For Representing  Certain Sets Of Strings In A Algebraic Function.

## Rules

1) Any Terminal Symbol i.e Symbols ε, Σ Including ∧(Empty) And Φ(Phi) Are Regular Expresions.

Example:- Input Symbols Like a,b,1,0,∧,Φ Are Regular Expresions

2) The Union Of Two Regular Expresions Is Also A Regular Expresion.

Example-R1,R2

(R1,R2) Is A Regular Expresion.

3) The Concatenation Of Two Regular Expressions Is Also A Regular Expresion.

Example- R1,R2—->(R1.R2)

4) The Iteration(Or Closure) Of A Regular Expresion Is Also A Regular Expresion.

Example-R—>R*(Closure Of R Is R*)

Example 2-a—>a*

a*={a,a,aa,aaa,……}

If ‘a’ Is The Regular Expresion a* Is The Closure Of ‘a'(Regular Expresion) a* Means The Set Of Strings Formed By ‘a’, Infinite Strings, See Below.

a*={∧,a,aa,aaa,aaaa,…} //   ∧ Is Empty String

If ‘a’ Is Regular Expresion Then Its Closure ‘a*’ Will Also Be Regular Expresion.

5) The Regular Expression Over Σ Are Precisely Those Obtained Recursively By The Application Of The Above Rules Once Or Several Times.

Means

This Rule Say’s

“All The Regular Expressions Over Sigma(Σ)

What Are They?

They Are Simply The Regular Expresions That Are Obtained By Applying The Rules 1,2,3,4 Which Are Given Above Once Or Many Times.

When We Do The Union Of Regular Expresion (or) Concatenation (or) Closure, We Will Get New Regular Expresions.

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