Infinite probabilistic and nonprobabilistic testing

We introduce three new notions of infinite testing for probabilistic processes, namely, simple, Buchi and fair infinite testing. We carefully examine their distinguishing power and show that all three have the same power as finite tests. We also consider Buchi tests in the non-probabilistic setting and show that they have the same distinguishing power as finite tests. Finally, we show that finite probabilistic tests are stronger than nondeterministic fair tests.