Home > Theory Of Computation > DFA Example : Construct Minimal Deterministic Finite Automata(FA) Σ={0,1} Such That a) String Start With 0 And Length Is Divisible By 3 b) String Start With 010 And Length Is Equal To 3(Mod 5)

# DFA Example : Construct Minimal Deterministic Finite Automata(FA) Σ={0,1} Such That a) String Start With 0 And Length Is Divisible By 3 b) String Start With 010 And Length Is Equal To 3(Mod 5)

Construct Minimal Deterministic Finite Automata(FA) Σ={0,1} Such That a) String Start With 0 And Length Is Divisible By 3 b) String Start With 010 And Length Is Equal To 3(Mod 5)

## a) String Start With 0 And Length Is Divisible By 3

Given Σ={0,1}

L={011,001,010,010000,010101010…..} // 011 Is Length 3, 001 Is Length 3, 010 Is The Length 3, 010101010 Is Length 9.

## b) String Start With 010 And Length Is Equal To 3(Mod 5)

There String Should Start With 010 And Length Is Equal To 3(Mod 5)

If I Divide Length With Mod 5, I Should Get Remainder As ‘3’

L={010,010,01000,01000010,…..} // 010 Is Length 3, 010 Is Length 3,01000 Is Length 5,01000010 Is Length 8.

If I Have Length ‘3’ And If I Do Mod 5, I’ll Get ‘3’

If I Have Length ‘8’ And If I Do Mod 5 I’ll Get ‘3’

If I Have Length ’13’ And If I Do Mod 5 I’ll Get ‘3’

If I Have Length ’18’ And If I Do Mod 5 I’ll Get ’13’

The Difference Between String lengths Is ‘5’