Regular expression in theory of computation solved examples Part 4

Solution:

We have the input alphabets ∑ = {0, 1}

Here, the resultant regular expression will denotes the set of strings of 1 in which number of 1’s equals 2 modulo 3 and it is followed by even number of 0’s.

Here, number of 1’s equals 2 modulo 3 means-

                        2          = 2
2 + 3    = 5

                        5 + 3    = 8

                        8 + 3    = 11

                        11 + 3  = 14

                        and soon.

The regular expression which represent the set of strings in which number of 1’s equal 2 modulo 3 can be written as –

                        11 (111)*

Also, the regular expression which represents the even numbers of 0’s can be written as-

                        (00)*

Thus, the resultant regular expression can be written as-

                        11 (111)* (00)*

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