WASHINGTON — After a laid-back night eating hot dogs and watching NCAA basketball in Dayton, Ohio, President Barack Obama and British Prime Minister David Cameron focused on their countries’ “rock-solid alliance” on the second day of Cameron’s official visit to the U.S.

Wednesday morning began as Cameron was formally welcomed to the White House by a large crowd and all the pomp of a state visit, although it was technically only an “official visit” because he is not considered the head of state. That title belongs to Queen Elizabeth II .

In meetings throughout the day, the two leaders discussed economic and foreign policy specifically regarding the Middle East and Afghanistan a couple months ahead of the NATO and G-8 summits. The timetable for the withdrawal for U.S. and U.K. troops in Afghanistan will be a major topic of discussion, and troops may be removed from lead combat roles as early as mid-2013.

“If we maintain a steady responsible transition… we can put Afghans in a position where they can deal with their own security,” Obama said in a press conference Wednesday afternoon.

This official visit followed the killings of 16 Afghan civilians last weekend allegedly by a lone U.S. soldier, and a roadside bomb blast that led to the deaths of six British troops last week.