"I believe it is possible to kill with compassion and in a non-violent way. An example would be a police officer that does so to protect another's life. Does this meet the definition of violence?" Kevin Leavitt
This does get tricky doesn't it? Compassion for the attacker or the people affected? I'm not sure how killing can be non-violent in any form. Even lethal injection to me is a violent act. The death touch by gradually shutting down organ systems over time, if you believe in it, is a violent act. This gets into the whole issue of harmony-does killing the attacker result in the best possible outcome? Or, is it better to simply restrain and contain the violent energy? We do that a lot with our prisons. We lock it up and put it out of our mind so as to not have to deal with it.
The police officer may be removing a violent threat from the situation-but to me the act of doing so, if it involves killing, is violent. That old Kwai Chang Caine/David Carradine comment something like this: to take another's life does no one honor. From a Buddhist perspective, this would fall into the issue of the karmic implications of the act.