[jprete]

I get your point, and my first question was "what operations are even atomic here for this problem to be well-defined?".

But I think "language operations are atomic and everything else isn't" is a reasonable inference for a puzzle.

I'm also intrigued by locking being done through atomic assignments; I thought it required at least something like "write if equal to value" or "write new value and return old".

[fjfaase]

The idea is that there is one task that does the locking. It does so by copying a value from a memory location A to B, when B is equal 0 (the initial value) at regular intervals. Any task that wants to get the lock, writes a unique task identifier (unequal to 0) to memory location A and starts polling B. When it becomes equal to its task identifier, it did get the lock. To release the lock, it writes 0 to B. If it did not get the lock and sees that B has become zero, and A is different, it may overwrite A with its own task identifier.

This locking is 'slow' and has 'unfair' behavior.

[fjfaase]

I think that the following PROMELA code proofs it:

    byte n = 0
    byte A = 0
    byte B = 0
    proctype Client(byte id)
    {
        do
        :: (A == 0) -> B = id
        :: (A == id) -> 
            n = n + 1;
            assert (n <= 1);
            n = n - 1;
            A = 0
        od
    }
    proctype LockServer()
    {
        do
        :: (A == 0) -> A = B
        od
    }
    init {
        atomic {
            run LockServer();
            run Client(1);
            run Client(2);
            run Client(3);
        }
    }

It fails when two 'Client(2)' is replaced by 'Client(1)'