We initiate the study of the trade-off between the length of a probabilistically checkable proof
of proximity (PCPP) and the maximal soundness that 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 deficiency as a function of the
proof-length and show that any verifier obtaining “best possible” soundness must query an …

We initiate the study of the tradeoff between the length of a probabilistically checkable proof
of proximity (PCPP) and the maximal soundness that 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 deficiency as a function of the
proof-length and show that any verifier obtaining “best possible” soundness must query an …