Certificate (complexity)

In computational complexity theory, a certificate (also called a witness) is a string that certifies the answer to a computation, or certifies the membership of some string in a language. A certificate is often thought of as a solution path within a verification process, which is used to check whether a problem gives the answer "Yes" or "No".

In the decision tree model of computation, certificate complexity is the minimum number of the ${\displaystyle n}$ input variables of a decision tree that need to be assigned a value in order to definitely establish the value of the Boolean function ${\displaystyle f}$.