We know that the exponential function $\exp(x,y) = x^y$ over natural numbers is not computable in polynomial time, because the size of the output is not polynomially bounded in the size of the inputs.Is this the main reason for the difficulty of computing the exponential function, or is exponentiation inherently difficult to compute, independently of this consideration?What is the complexity of the bit graph of the exponential function?   $$\{\langle x,y,i \rangle \mid x,y,i\in\mathbb{N} \text{ and the $i$-th bit of $x^y$ is $1$} \}$$
Complexity of exponential function
cc.complexity theory;nt.number theory