Verification Algorithms

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(n²)

• 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 $\in$ {0,1}* $\mid$ there exists y $\in$ {0,1}* such that A(x,y) = 1}