May a correct program be incorrectly synchronized?

Question

In answer of Does a correctly synchronized program still allow data race?(Part I), it gives us a good example: all executions of a program appear to be sequentially consistent, but it still has data race. It tells us why another direction of following conclusion in JLS is not true:

If a program has no data races, then all executions of the program will appear to be sequentially consistent.

Now take a look at another conclucsion in JLS:

A program is correctly synchronized if and only if all sequentially consistent executions are free of data races.

According to this conclusion,above example is not correctly synchronized, so may a correct program be incorrectly synchronized?

Answer 1

You would probably need to define first what a correct program is (not easy). JCiP proposes (in a different context):

a program is correct if it conforms to its specifications.

Using that definition, the example provided is correct. However, it is not correctly synchronized (there is a data race on hash).

==> a correct program may be incorrectly synchronized, as proved by that example.

Answer 2

While this doesn't appear to answer the OP's question, I am keeping it for the comments.

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You can get a number of race conditions using synchronized collections. e.g.

Vector<Integer> vector = ...
vector.add(1);

vector.set(0, 1 + vector.get(0));

Each method is synchronized and yet there is a race condition. This is because you can have threads T1 and T2 doing.

T1: int tmp1 = vector.get(0);
T2: int tmp2 = vector.get(0);
T1: vector.set(0, 1 + tmp1);
T2: vector.set(0, 1 + tmp2);

In this case tmp1 == tmp2 which is not normally the case.

To synchronize this correctly you would do the following to ensure you hold the lock the whole time.

synchronized(vector) {
    vector.set(0, 1 + vector.get(0));
}