I am confused if "state" should take an "s" or not in the following sentence:
… at a given time-slot, the knowledge of the state(s) of all the machines in …
Each machine has one 'state' at each time-slot. This 'state' can change from machine to machine at the same time-slot and from slot to slot for the same machine.
Best Answer
In this context, we can assume that each machine has its state, so it's correct to use states as we're talking about different entities (machines) with different and independent aspects (states), even if they were the same state in all machines.
On the other hand, if we were talking about the general state of the set of machines, then the plural would be wrong, considering we're yet talking about different entities (machines) but they have aspects (state) which are dependent on each other.