Consider a corresponding verification problem for HAM-CYCLE:

Given a cycle and a graph G, verify if cycle is a Hamiltonian cycle in G.

Running time: O(*n*^{2})

- A
**verification algorithm**is a two-argument algorithm A, where one argument is an ordinary input string x, and the other argument is a binary string y called a**certificate**. Algorithm A**verifies**x if there exists a y such that A(x,y) = 1.

- The
**language verified**by a verification algorithm A is

L = {x {0,1}* there exists y {0,1}* such that A(x,y) = 1}