A decision problem is a subset $~$D$~$ of a set of instances $~$A$~$, where generally $~$A$~$ is the set of finite bitstrings $~$\\{0,1\\}^\*$~$\.

Why is it called a *decision problem*? As a reader looking for an intuitive understanding, that's one of the first questions I want answered.

Is it about deciding things? Is "Where should we go to eat tonight?" a decision problem? :-)