DFA / Deterministic Finite Automaton



DFA

  • In DFA, every state will have a single transition for every symbol.

  • ϵ- moves is not accepted in DFA

  • So, the transition table will not have ø

  1. Construct DFA with its transition graph and transition table for the RE (0+1)* 01
    Here , Σ= {0,1}

Transition graph

Transition table

 

0

1

qo

q1

q0

q1

q1

q2

q2*

q1

q0

Note:
In DFA, each entry of the transition table will have exactly one entry

  1. Construct DFA with its transition graph and transition table for the RE (a+b)* abb
    Here, Σ= {a,b}

Transition graph

Transition table

 

a

b

q0

q1

q0

q1

q1

q2

q2

q2

q3

q3*

q1

q0

  1. Construct DFA with its transition graph and transition table for the RE (a | b)* abba
    Here, Σ= {a,b}

​​​​​​​Transition graph

Transition table

 

a

b

q0

q1

q0

q1

q1

q2

q2

q1

q3

q3

q4

q0

q4*

q2

q0

  1. Construct DFA with its transition graph and transition table for the set of strings over {0,1} whose length is divisible by 4.

Transition graph

Transition table

 

a

b

q0*

q1

q1

q1

q2

q2

q2

q3

q3

q3

q0

q0

  1. Construct DFA with its transition graph and transition table for the regular expression 
    a b(a | b)*

Transition graph

Transition table

 

a

b

1

2

DS

2

2

3

3*

DS

DS

DS

DS

DS

DS represents Dead State

  1. Construct DFA with its transition graph and transition table for  L={ an bm cp | n,m,p ≥ 1 }

Transition graph

Transition table

 

a

b

c

1

2

DS

DS

2

2

3

DS

3

DS

3

4

4*

DS

DS

4

DS

DS

DS

DS

DS represents Dead State