In complexity theory, UP ("Unambiguous Non-deterministic Polynomial-time") is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine where there exists exactly one accepting path if the string is accepted. This is a Subset (though not necessarily proper) of NP and a Superset (though not necessarily proper) of P.

A language L belongs to UP if there exists a two input polynomial time algorithm A and a constant c such that

L = {x in {0,1}* | ∃! certificate, y with |y| = O(x^c) such that A(x,y) = 1}

Algorithm A verifies L in polynomial time.