Editing Function problem (section)

== Total function problems ==
The relation <math>R(x, y)</math> used to define function problems has the drawback of being incomplete: Not every input <math>x</math> has a counterpart <math>y</math> such that <math>(x, y) \in R</math>. Therefore the question of computability of proofs is not separated from the question of their existence. To overcome this problem it is convenient to consider the restriction of function problems to total relations yielding the class '''[[TFNP]]''' as a subclass of '''FNP'''. This class contains problems such as the computation of pure [[Nash equilibria]] in certain strategic games where a solution is guaranteed to exist. In addition, if '''TFNP''' contains any '''FNP-complete''' problem it follows that <math>\mathbf{NP} = \textbf{co-NP}</math>.