Function problem

In computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem. For function problems, the output is not simply 'yes' or 'no'.

A functional problem ${\displaystyle P}$ is defined as a relation ${\displaystyle R(x,y)}$ over a cartesian product over strings of an arbitrary alphabet ${\displaystyle \Sigma }$:

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