Connecting this definition with other definitions of RP, co-RP and ZPP is easy. The probabilistic polynomial-time Turing Machine "V*w"("x") corresponds to the deterministic polynomial-time Turing Machine "V"("x", "w") by replacing the random tape of "V*" with a second input tape for V on which is written the sequence of coin flips. By selecting the witness as a random string, the verifier is a probabilistic polynomial-time Turing Machine whose probability of accepting x when x is in "X" is large (greater than 1/2, say), but zero if "x" ∉ "X" (for RP); of rejecting x when x is not in X is large but zero if "x" ∈ "X" (for co-RP); and of correctly accepting or rejecting "x" as a member of "X" is large, but zero of incorrectly accepting or rejecting x (for ZPP).