Editing Computational complexity theory (section)

===Decision problems as formal languages===
[[Image:Decision Problem.svg|thumb|A [[decision problem]] has only two possible outputs, ''yes'' or ''no'' (or alternately 1 or 0) on any input.]]
[[Decision problem]]s are one of the central objects of study in computational complexity theory. A decision problem is a type of computational problem where the answer is either ''yes'' or ''no'' (alternatively, 1 or 0). A decision problem can be viewed as a [[formal language]], where the members of the language are instances whose output is yes, and the non-members are those instances whose output is no. The objective is to decide, with the aid of an [[algorithm]], whether a given input string is a member of the formal language under consideration. If the algorithm deciding this problem returns the answer ''yes'', the algorithm is said to accept the input string, otherwise it is said to reject the input.

An example of a decision problem is the following. The input is an arbitrary [[graph (discrete mathematics)|graph]]. The problem consists in deciding whether the given graph is [[connectivity (graph theory)|connected]] or not. The formal language associated with this decision problem is then the set of all connected graphs — to obtain a precise definition of this language, one has to decide how graphs are encoded as binary strings.