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In my opinion, it is better to implement timers with threads. In your case I would have a class that implements a function that simply waits some time and that can be stopped. If it arrives to the timeout, it turns your variable to False. If you receive a new string, you stop the thread and start it again.

Something like this

@staticmethod
def watch_until_string_a(max_time_stopped, stop):
    old_time = rospy.Time.now().to_sec()
    diff_time = 0

    while diff_time < max_time_stopped and not stop():
        time.sleep(0.2)
        diff_time = rospy.Time.now().to_sec() - old_time

    if not stop():
        self.a_current = False

then you can start a timer just by doing

    th = threading.Thread(target=self.watch_until, args=(time_before, lambda: stop[0]))
    th.start()

with stop being a list of a single boolean

   stop = [False]

If you want to stop your thread, you just have to change the value of stop to

   stop = [True]

and you thread will stop without changing the value of the variable. Then just wait for them to finish

   th.join()

and you can launch it again.

The code above is for a single string, but you can easily modify it to be used with the two strings (remember that you will need one thread per string). I hope it helps.