#Automatacodingquestions

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Power Of Alphabets In Automata

Power Of Alphabets (∑) In Automata, If ∈ Is An Alphabet Then ∑k 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             Read the full article