Provide the regular expression RE defined over ∑= {0,1} for the strings belonging to the following languages:

Provide the regular expression RE defined over ∑= {0,1} for the strings belonging to the following languages: 

a.    All strings having zeros in multiples of three.

b.    All strings do not start with double zero.

c.    All strings starting with zero have no consecutive 1’s in them.

Solution

a.    All strings having zeros in multiples of three.

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

b.    All strings that do not start with double zero.

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

 c.    All strings starting with zero have no consecutive 1’s in them.

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