FAQs

Is it numerically stable?

We try to make AITIP as numerically stable as possible, but you are responsible for making sure that your inputs are not ill-formatted. For example, please try to make sure that your parameters do not contain values that are very large or very close to zero (e.g., `1^10`, `1^{-10}`). If you have rational numbers in your parameters, please write them down in higher precision (e.g., `0.333333333` is a better representation of `1/3` than `0.333`). If possible, you should eliminate the rounding problems altogether by reformulating your input inequality and constraints.

How many random variables can it handle?

For this web service, we set a hard limit of `12` for the maximum number or random variables, as the computing server is running on a cheap single CPU machine on Google Cloud. If you need to prove larger problems, please download and compile the source code and run it on your own machine (preferably with a GPU). On our test machine with a RTX 2080 Ti installed, AITIP can reliably prove inequalities involving up to `15` random variables. The complete source code is available on GitHub