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# Construct The Minimal Finite Automata And Find The Number Of States In Following Language

Construct The Minimal Finite Automata And Find The Number Of States In Following Language

L={ambn/m≥0,n≥2018}

This Is A Interesting Problem.

Given m≥0

n≥2018 // 2018 Is A Big Number, It Becomes Very Big DFA But We Need Minimal DFA.

Σ={a,b}

m≥0 Let n≥1

So My Language Is

L={b,bb,bbb,bbbb…….} // ε Epsilon Is Not There Because m=0,n=0,n=1 means ‘b’

i)

ii) m≥0,n≥2

So My Language Is

L ={bb,bbb,bbbb….}

By Seeing These Two Diagrams I’m Not Able To Guess How Many No. Of States, I Can Get In DFA For m≥0,n≥2018

Lets Take One More Example.

m=0,n≥3

iii) L={bbb,bbbb,bbbbb,…….}

If You Observe (i),(ii),(iii) I’m Increasing The ‘n’ Value The No.Of States For DFA’s Are Increasing 3,4,5….

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