Let's say we have a program that only accepts numerical inputs and the output is simply an increment by one of the input.
Example with input "a" and output "b":
$$Input: a = 7$$
$$Output: b= a+1 = 8$$
So it would be easy to know what the program is doing.
Is it possible to obfuscate the program code in such a way that we can never be sure how it's done?
For example our program could take the input:
subtract input - 1
$$14 - (7 - 1) = 8$$
Is it possible to obfuscate the exact functionality, so that it can't be reverse-engineered? If not: Could such an obfuscation scheme exist one day or is there something fundamental that prevents it?