Inspired from this and the similar questions, I want to learn how does mt19937 pseudo-number generator in C++11 behaves, when in two separate machines, it is seeded with the same input.
In other words, say we have the following code;
std::mt19937 gen{ourSeed};
std::uniform_int_distribution<int> dest{0, 10000};
int randNumber = dist(gen);
If we try this code on different machines at different times, will we get the same sequence of randNumber values or a different sequence each time ?
And in either case, why this is the case ?
A further question:
Regardless of the seed, will this code generate randomly numbers infinitely ? I mean for example, if we use this block of code in a program that runs for months without stopping, will there be any problem in the generation of the number or in the uniformity of the numbers ?
The generator will generate the same values.
The distributions may not, at least with different compilers or library versions. The standard did not specify their behaviour to that level of detail. If you want stability between compilers and library versions, you have to roll your own distribution.
Barring library/compiler changes, that will return the same values in the same sequence. But if you care write your own distribution.
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All PRNGs have patterns and periods. mt19937 is named after its period of 2^19937-1, which is unlikely to be a problem. But other patterns can develop. MT PRNGs are robust against many statistical tests, but they are not crytographically secure PRNGs.
So it being a problem if you run for months will depend on specific details of what you'd find to be a problem. However, mt19937 is going to be a better PRNG than anything you are likely to write yourself. But assume attackers can predict its future behaviour from past evidence.