Automata for given Regular Expression

Question

Can you please draw the DFA for given regex (ab*)*

Comments

When I tried on JFLAP conversion the RE i get is this (λ+a+(a+a)bb*)*(λ+a+(a+a)bb*)

Is this correct please reply

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This is not the correct answer since the question clearly asked to draw a DFA. In the diagram above, for every input symbol, i.e, there is no transition from state q0 on input symbol ‘b’ and similarly there is also no transition from state q1 on input symbol ‘a’.

Answer 1

 DFA  is as :

Comments

Can not start from b

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Thats why b is on dead state