.
messages 𝑚₁, 𝑚₂, …, 𝑚ⱼ have been sent from the verifier, is defined to be the response of the query to the PCP on input (𝑖,𝑗,𝑚₁,𝑚₂,…, 𝑚ⱼ). The assumption that the provers cannot communicate is a powerful one. As you might remember from Part III: Zero-Knowledge, Goldreich, Micali, and Wigderson have