How Will the US Respond to a North Korean Attack on South Korea?

What will the United States do if there is a live-fire exchange between North and South Korea?

There has been a lot of "pooh poohing" of the rants / threats coming out of South Korea in recent days, with the White House even saying there is "no evidence that the country’s leader, Kim Jong-un was mobilizing troops or other military forces for any imminent attack.

Yet, at the same time, the US has moved a Navy destroyer off the coast of North Korea and has made mock bombing runs over South Korea with its B-2 stealth bombers, a highly unusual move for the US.

While the US has made these moves (along with its 28,500 troops stationed in South Korea), the military of North Korea says it is at its highest level of alertness, and continues to insist that a state of war exists between the two Koreas.

Equally disturbing is the fact that South Korean President Park Geun-hye has ordered her military to "deliver a strong and immediate response to any North Korean provocation."  In fact, she has said (rightly so), "If the North attempts any provocation against our people and country, you must respond strongly at the first contact with them without any political consideration."

This contrasts with the stance historically taken by South Korean.  Park is taking a much harder stance than her predecessor, Lee Myung-bak, who did not respond after a 2010 North Korean artillery attack killed four South Koreans.

So, we currently have:

• An unpredictable N. Korean making military threats against S. Korea and the US
• The US moving warships and planes into the region and conducting maneuvers there
• S. Korea pledging to respond to any attack militarily
• Reports of the Chinese military mobilizing near the border with N. Korea
• N. Korea reportedly re-starting a shuttered nuclear reactor

If the two countries trade missiles, bombs or gunfire, how will the United States respond given the currently explosive situation on the Korean peninsula?  A military exchange could take place by accident or on purpose.  No matter what the provocation, with 28,500 American troops in South Korea, would the US be forced to attack North Korea?

If US troops were targeted, or accidentally harmed, what would be the United States' response?  

Further, if the North attacks the South, it appears that military leaders in the south have been given the "green light" by their civilian leadership to respond, unilaterally.

This has all the makings of a catastrophe just waiting to happen, if one or more of the players makes a misstep.