Question

Which of the following REs correspond to the same language? I. (00)*(ε + 0) II. (00)*...

Which of the following REs correspond to the same language?

I. (00)*(ε + 0)

II. (00)*

III. 0(00)*

IV. 0*

Homework Answers

Answer #1

Option I

(00)*(ε + 0)

The language generated by this RE is (00)n 0 where n>=0

=> The strings generated are : {0, 000, 00000, 0000000, ......} ie strings containing odd number of zeroes

Option II

(00)*

The language generated by this RE is (00)n where n>=0

=> The strings generated are : {00, 0000, 000000, ......} ie strings containing even number of zeroes

Option III

0(00)*

The language generated by this RE is 0 (00)n where n>=0

=> The strings generated are : {0, 000, 00000, 0000000, ......} ie strings containing odd number of zeroes

Option IV

0*

The language generated by this RE is 0n  where n>=0

=> The strings generated are: {0, 00, 000, 0000, ....} ie strings containing both odd and even number of zeroes

=> Therefore Option I and Option III are generating the same language.

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