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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.
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