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# DFA Example : Construct The Minimal Finite Automata And Find Number Of States In The Following

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

## i) L={ambn/m,n≥0}

Patter Question

a=input symbol

b=input symbol

m&n≥0

So My Language Is

L={ε,a,b,ab,aab,aaab,aaabbb……} // Infinite String

Explanation Of Language

m,n Can Be ‘0’ (zero)

m can be ‘1’ or ‘2’ or ‘3’……

n can be ‘1’ or ‘2’ or ‘3’…….

If m,n is ‘0’(zero) then a0b0  Becomes (0), Means ε(Epsilon)

If m is 1 and n is 1 then a,b

If m is 2 and n is 2 then aa,bb

## ii) L={am/m≥0}

a=Input Symbol

m≥0

So My Language Is L={ε,a,aa,aaa,…..}

Language Explanation

If m=0, Then aBecomes zero(0) Means ε (Epsilon)

If m=1, Then a1, Then a1=a

if m=2, Then athen a2=aa

## iii) L={ambncp/m,n,p≥0}

a,b,c Are Input Alphabets.

mnp Are ‘powers’

mnp≥0

If m is 0 And n Is 0 And p Is 0.

a0b0c0=0 Means ε(Epsilon)

I’ll Get ε