When it comes to scheduling some definitions should be completely understood. Schedulabiltiy test is one of them.
There is a book from Sanjoy K. Baruah (Multiprocessor Scheduling for Real-Time Systems) which explains Schedulabilty test as follows:
Let A denote a scheduling algorithm. A sporadic task system T is said to be A-schedulable, if A meets all deadlines when scheduling each of the potentially infiinte different collection of jobs that could be generated by T [...]
There is also a distinction between exact and sufficient for Schedulability tests:
A schedulabiltiy test is called exact, if it identifies all A-schedulable systems. The test is called sufficient, if it identifies some A-schedulable systems.
So, informally speaking, I can say, that a (in)equation which uses the parameters of the task system T (e.g. periods, deadlines) to make a statement about the schedulabiltiy is a Schedulability test. So far I have understood.
But what does exact and sufficient mean in this context? For me, some algorithm is either schedulable or not (for all different collections of jobs). Can somebody give me an example or explain it in a simple way?
You already have the definition.
An exact test will give you ALL schedulable systems.
A sufficient test can give you one and then stop.
Say you need to schedule 3 jobs. You need to run them one by one and there are no other constraints (any ordering works).
A sufficient test will tell you that you can schedule them in order 1,2,3.
A exact test will tell list all possible combinations of jobs.