Abstract
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 exponentially long proof. © 2008 Springer-Verlag.
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CITATION STYLE
Ben-Sasson, E., Harsha, P., Lachish, O., & Matsliah, A. (2008). Sound 3-query PCPPs are long. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5125 LNCS, pp. 686–697). https://doi.org/10.1007/978-3-540-70575-8_56
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