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

Question

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.

Republic

See also this question . – Grenadine

chirs view my updated answer I corrected DFA – Grenadine

Determinicy refers to the fact that it is not allowed to have two outgoing transitions with the same label from the same state. It does not refer to incomming transitions. – Sanders

Answer 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.

Grenadine

I believe it is 0(0+1)*0+1(0+1)*1 instead of 0(1 + 0)*0 + 1(1 + 0)*1 – Michelinemichell

@HélioSantos Is there any difference? – Republic

yes, its a regular expression, not a math expression. (0+1) => one or more zeroes followed by a one (1+0) => one or more one followed by a zero – Michelinemichell

@HélioSantos Yes it is a regular expression. I think (0+1)* means any number of zeroes and ones, same as (1+0)* . From your point, my regular expression doesnot accept 0010, but it does. – Republic

@Republic that would be [01]* any number of zeroes OR ones (01|10)* any number of the combination 01 OR 10. Try here(rubular.com). Which regex implementation are you using? – Michelinemichell

@HélioSantos (0 + 1)* means any string consist of 0s and 1s including ^ and (O+1)* = (1+0)*. Actually + means Union and A U B = B U A. – Grenadine

@GrijeshChauhan + is a quantifier. The element before + should appear one or more times (regular-expressions.info/repeat.html). Are we talking about the same thing - regex?? – Michelinemichell

@HélioSantos meaning of plus depends on syntax it appears if expression is a+ this means one of more as and if a+b then + means Union operation either a or b. – Grenadine

@HélioSantos + in Regular Expression – Grenadine

@HélioSantos Welcome your! :) – Grenadine

Answer 2

I think you should start with 0 first

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

Ramey

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