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* The algorithm that reads ''n'' numbers and then computes <math>2^{2^n}</math> by [[repeated squaring]] runs in polynomial time in the Arithmetic model, but not in the Turing model. This is because the number of bits required to represent the outcome is exponential in the input size.
However, if an algorithm runs in polynomial time in the arithmetic model, and in addition, the binary length of all involved numbers is polynomial in the length of the input, then it is always polynomial-time in the Turing model. Such an algorithm is said to run in [[Strongly polynomial|strongly polynomial time]].
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