If you want to know whether two sequences are outputs of the same computer program with different seeds, then I doubt you can do much better than enumerating all computer programs and trying them. This can't be done in practice. Some preudo-random number generators work reasonably well with one seed, and terribly with other seeds, which means the same algorithm with different seeds can produce either a sequence which looks random or Bach's suites for solo cello.

Perhaps you want the idea of a randomness test, such as Marsaglia's Diehard tests. The reason there are so many, including many silly tests, is that pseudo-random numbers which appear uniform often fail catastrophically when they are used to generate a sequence of pseudo-random numbers.

Another possible interpretation is to say that you have a particular distribution, perhaps the uniform distribution. You can test whether a sample is consistent with that distribution, e.g., with the Pearson chi-squared test. If you have two samples, you can estimate a distribution from the first sample and test whether the second sample is consistent with this. Since you talk about identifying when you switch from one generator to another in a sequence, you may want to look at what is called "structural change" or "change points" in statistics. There are automated tests for this which assume that the generators are not even uniform.

If you want to know whether two sequences are outputs of the same computer program with different seeds, then I doubt you can do much better than enumerating all computer programs and trying them. This can't be done in practice. Some preudo-random number generators work reasonably well with one seed, and terribly with other seeds, which means the same algorithm with different seeds can produce either a sequence which looks random or Bach's suites for solo cello.

Perhaps you want the idea of a randomness test, such as Marsaglia's Diehard tests. The reason there are so many, including many silly tests, is that pseudo-random numbers which appear uniform often fail catastrophically when they are used to generate a sequence of pseudo-random numbers.

Another possible interpretation is to say that you have a particular distribution, perhaps the uniform distribution. You can test whether a sample is consistent with that distribution, e.g., with the Pearson chi-squared test. If you have two samples, you can estimate a distribution from the first sample and test whether the second sample is consistent with this. Since you talk about identifying when you switch from one generator to another in a sequence, you may want to look at what is called "structural change" or "change points" in statistics. There are automated tests for this which assume that the generators are not even uniform.

If you want to know whether two sequences are outputs of the same computer program with different seeds, then I doubt you can do much better than enumerating all computer programs and trying them. This can't be done in practice, and in theory you will have difficulty concluding that two programs produce the same output since you can't solve the halting problem or compute an upper bound for the busy beaver function. Some preudo-random number generators work reasonably well with one seed, and terribly with other seeds, which means the same algorithm with different seeds can produce either a sequence which looks random or Bach's suites for solo cello.

Perhaps you want the idea of a randomness test, such as Marsaglia's Diehard tests. The reason there are so many, including many silly tests, is that pseudo-random numbers which appear uniform often fail catastrophically when they are used to generate a sequence of pseudo-random numbers.

Another possible interpretation is to say that you have a particular distribution, perhaps the uniform distribution. You can test whether a sample is consistent with that distribution, e.g., with the Pearson chi-squared test. If you have two samples, you can estimate a distribution from the first sample and test whether the second sample is consistent with this. Since you talk about identifying when you switch from one generator to another in a sequence, you may want to look at what is called "structural change" or "change points" in statistics. There are automated tests for this which assume that the generators are not even uniform.

If you want to know whether two sequences are outputs of the same computer program with different seeds, then I doubt you can do much better than enumerating all computer programs and trying them. This can't be done in practice. Some preudo-random number generators work reasonably well with one seed, and terribly with other seeds, which means the same algorithm with different seeds can produce either a sequence which looks random or Bach's suites for solo cello.

Perhaps you want the idea of a randomness test, such as Marsaglia's Diehard tests. The reason there are so many, including many silly tests, is that pseudo-random numbers which appear uniform often fail catastrophically when they are used to generate a sequence of pseudo-random numbers.

Another possible interpretation is to say that you have a particular distribution, perhaps the uniform distribution. You can test whether a sample is consistent with that distribution, e.g., with the Pearson chi-squared test. If you have two samples, you can estimate a distribution from the first sample and test whether the second sample is consistent with this. Since you talk about identifying when you switch from one generator to another in a sequence, you may want to look at what is called "structural change" or "change points" in statistics. There are automated tests for this which assume that the generators are not even uniform.