It is important to understand the different types of DoS attacks and the symptoms of those attacks. Leaving a connection half open is a symptom of which type of attack?

SYN flood attack.

Explanation:

Doing this is a symptom of an SYN flood attack. Attackers performing this type of DoS attack will try and open as many connections as possible but never fully finish the connection. This ultimately causes the system to use all of its computing power to try to resolve these failed connections which would cause the system to crash or become unresponsive. Therefore, denying service to potential clients if done correctly. This is just one of the many types of DoS attacks that exist.