Definition
A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as: the set of inputs for which the problem returns yes.
These inputs can be natural numbers, but may also be values of some other kind, such as strings over the binary alphabet {0,1} or over some other finite set of symbols. The subset of strings for which the problem returns "yes" is a formal language, and often decision problems are defined in this way as formal languages.
Alternatively, using an encoding such as Gödel numberings, any string can be encoded as a natural number, via which a decision problem can be defined as a subset of the natural numbers.
Read more about this topic: Decision Problem
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