1. [5 points] Let T be the set of strings whose alphabet is {0,1, 2, 3} such that, in every element of T, a. Every 1 is followedimmediately by exactly one 0. b. Every 2 is followed immediately byexactly two 0s. c. Every 3 is followed immediately by exactly three0s. (For instance, 00103000 ∈ T.) Find a recursive definition forT.
Answer
a) (0+10+2+3)* where + means union and * is kleene star
b) (0+1+200+3)*
c) (0+1+2+3000)*
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