Q1. Which two of the following four regular expressions are equivalent? (ε is the empty string).

(i) (00)*(ε + 0)
(ii) (00)*

(iii) 0*

(iv) 0(00)*

Q1. Which two of the following four regular expressions are equivalent? (ε is the empty string).

(i) (00)*(ε + 0)
(ii) (00)*

(iii) 0*

(iv) 0(00)*

1.) 0^n where n>=0

2.) 0^2n where n>=0

3.) 0^n where n>=0

4.) 0^2n+1 where n>=0

So ans is 1 and 3

None

Strings generated by expressions are:

(i) (00)(ε + 0) : **00 , 000**

(ii) (00) : **00**

(iii) 0* : **e, 0 , 00, 000 , 0000, 00000 …**.

(iv) 0(00)* : **0 , 000 , 00000 , 0000000 …**

hence no two expressions are generating same languages

None of the RE’s are equivalent.

here’s why…

- (00)(ε+0): 00,000

Explanation: Either one of ε or 0 will become the second character.So only above two strings are accepted. - (00) : 00

Explanation: The only accepted string is 00 as string 00 is parenthesized - 0* : ε,0,00,000…

Explanation: Any number of zeroes are accepted in the string but only zeroes - 0(00)* : 0,000,00000…

Explanation: Strings with odd number of zeroes will be accepted by this RE as first 0 will compulsorily appear in all strings followed by any number of 00