Home > Theory Of Computation > Day 3: Power Of Alphabets In Automata

Day 3: Power Of Alphabets In Automata

Power Of Alphabets (∑) In Automata, If ∈ Is An Alphabet Then ∑Is The Set Of All The String From The Alphabet ∈ Of Length Exactly k.

Example – ∑= {a,b}  // a & b are input alphabets

We Are Talking About ∑k  (Sigma To The Power Of k)

 

∑ 1= Set Of All The String Of Length 1.

={a,b} // Formed String

 

∑ 2= Set Of All The String Of Length 2.

={aa,ab,ba,bb} // Formed Strings

 

∑ 3= Set Of All The String Of Length 3.

={aa,ab,ba,bb,aab,aba,baa,bba} // Formed Strings

 

∑ 0= Set Of All The String Of Length 0 (Empty Set)

={∈} // Empty Set Or Epsilon

 

 

Positive Closure Of  ∑

∑+=∑1 ∪ ∑2∪ ∑3∑4……

Kleen Closure Of  ∑

∑*= ∑0 Σ1 ∪ ∑2∪ ∑3∑4……

// Kleen Closure Of  ∑ Is A ∪niversal Language

 

To Remember The Above, Remember The Following Rules

(a)  ∑+ ⊂ ∑*  

// Sigma To The Power Of Plus Is The Subset Of SigmaTo The Power Of Star

(b) ∑* = ∑+ ∪ {∈}

// Sigma To The Power Of Star Is Equal To Sigma To The Power Of Plus ∪nion Epsilon ( Empty Set)

(c) ∑+ = ∑*- {∈}

(d) ∑* ∪ ∑+ = ∑*

(e) ∑* ∩ ∑+ = ∑+

(f) ∑* ∑+ = ∑+

(g) ∑* ∑* = ∑*

(h) ∑+ ∑+ = ∑+ – ∑1

 

 

 

 

 

 

Leave a Reply