> Within cryptography, yes, but in programming in general, absolutely not.
I cannot think of any algorithms with arbitrary sized inputs that have truly constant execution time. The reason for that I do not find this possible with classical computers is that no matter what you do, reading data from memory is an unavoidable variable time process.
Do not that arbitrary sized inputs here imply that the input is meaningful and must all be processed. I do not see algorithms that do not process their inputs as candidates here, such as the elsewhere stated example of even/odd test which just read a single bit. I consider an algorithm that only reads a fixed amount of information from its input to be a fixed-input algorithm, regardless of the "full" size of its input.
Of course, if you place an upper bound on the input, then you can pad in various ways, or possibly have algorithms whose execution time is inversely proportional to its input size, thus balancing itself. However, placing an upper bound also mean violating the "arbitrary" requirement entirely, thus disqualifying the algorithm.
Do note that I'd actually be quite interested if you have examples of such algorithms.
> I cannot think of any algorithms with arbitrary sized inputs that have truly constant execution time.
With respect, I think you may misunderstand the meaning of "constant time" in the sense of complexity theory, i.e. O(1). Accessing an element in an array of size n is a constant time operation. See: https://stackoverflow.com/questions/7297916/why-does-accessi...
Wouldn’t searching for an element in an arbitrary array of size n happen in O(n) time, while only accessing it is considered O(1)? I could understand the search case for something like a hash table being O(1) but does that also apply to your standard array?
So binary search is not logn time because it only reads logn values from the input? To know which parts are not read you basically have to run the algorithm. I find your definition unhelpful.
I cannot think of any algorithms with arbitrary sized inputs that have truly constant execution time. The reason for that I do not find this possible with classical computers is that no matter what you do, reading data from memory is an unavoidable variable time process.
Do not that arbitrary sized inputs here imply that the input is meaningful and must all be processed. I do not see algorithms that do not process their inputs as candidates here, such as the elsewhere stated example of even/odd test which just read a single bit. I consider an algorithm that only reads a fixed amount of information from its input to be a fixed-input algorithm, regardless of the "full" size of its input.
Of course, if you place an upper bound on the input, then you can pad in various ways, or possibly have algorithms whose execution time is inversely proportional to its input size, thus balancing itself. However, placing an upper bound also mean violating the "arbitrary" requirement entirely, thus disqualifying the algorithm.
Do note that I'd actually be quite interested if you have examples of such algorithms.