Do two synchronized methods execute simultaneously

If t1 access the m1 method (synchronized method), could t2 thread access m2 method (synchronized method) simultaneously?

The synchronized keyword applies on object level, and only one thread can hold the lock of the object. So as long as you’re talking about the same object, then no, t2 will wait for t1 to release the lock acquired when it entered m1.

The thread can however release the lock without returning from the method, by calling Object.wait().

If not, what would be the state of t2 ?

It would sit tight and wait for t1 to release the lock (return from the method or invoke Object.wait()). Specifically, it will be in a BLOCKED state.

Thread state for a thread blocked waiting for a monitor lock. A thread in the blocked state is waiting for a monitor lock to enter a synchronized block/method or reenter a synchronized block/method after calling Object.wait.

Sample code:

public class Test {

    public synchronized void m1() {
        try { Thread.sleep(2000); }
        catch (InterruptedException ie) {}
    }

    public synchronized void m2() {
        try { Thread.sleep(2000); }
        catch (InterruptedException ie) {}
    }

    public static void main(String[] args) throws InterruptedException {
        final Test t = new Test();
        Thread t1 = new Thread() { public void run() { t.m1(); } };
        Thread t2 = new Thread() { public void run() { t.m2(); } };

        t1.start();
        Thread.sleep(500);

        t2.start();
        Thread.sleep(500);

        System.out.println(t2.getState());
    }
}

Output:

BLOCKED