Question: Problem 2 Consider the language F = { 0 x : x is the nth Fibbonacci number, n 0 } where the Fibbonacci sequence :

Problem 2 Consider the language
F ={0 x : x is the nth Fibbonacci number, n 0}
where the Fibbonacci sequence : 1,1,2,3,5,8,13,21,... is given by the rule
f ib(0)=1, f ib(1)=1, f ib(x +2)= f ib(x)+ f ib(x +1)
Observe that the gap between any two members is equal to the preceding member. Use the Myhill-Nerode theorem to show F is not regular.

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