What will be the DFA for the regular expression 0(0+1)*0+1(0+1)*1?

问题

This is the DFA i have drawn-

Is it correct?
I am confused because q4 state has 2 different transitions for same input symbol which violates the rule of DFA, but I can't think of any other solution.

回答1:

Your DFA is not correct.
_{your DFA is completely wrong so I don't comment}

DFA for RE:

0(1 + 0)*0 + 1(1 + 0)*1  

Language Description: if string start with 0 it should end with 0 or if string start with 1 it should end with 1. hence two final states (state-5, state-4).

state-4 : accepts 1(1 + 0)*1
state-5 : accepts 0(1 + 0)*0
state-1 : start state.

DFA:

EDIT :

+ Operator in Regular Expression

(0 + 1)* = (1 + 0)* that is any string consist of 1s and 0s, including Null string ^.

Here + means Union if it appear between two RE: and A U B = B U A (similarly)=> (0 + 1) = (0 + 1) .

_{meaning of plus + depends on syntax it appears in: If expression is a⁺ (+ is superscripted) this means one of more as, and If a+b then + means Union operation either a or b.}

a+ : { a, aa, aaa, aaa.....} that is any number of a string in language with length > 1.

回答2:

I think you should start with 0 first

0(1 + 0)*0 + 1(1 + 0)*1

来源：https://stackoverflow.com/questions/14122755/what-will-be-the-dfa-for-the-regular-expression-00101011