Sound 3-Query PCPPs Are Long

We initiate the study of the tradeoff between the lengthof a probabilistically checkable proof of proximity (PCPP) and the maximal soundnessthat can be guaranteed by a 3-query verifier with oracle access to the proof. Our main observation is that a verifier limited to querying a short proof cannot obtain the same soundness as that obtained by a verifier querying a long proof. Moreover, we quantify the soundness deficiencyas a function of the proof-length and show that any verifier obtaining "best possible" soundness must query an exponentially long proof.

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