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Doubly Sub-Linear Interactive Proofs of Proximity

Authors Noga Amir, Oded Goldreich , Guy N. Rothblum

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Author Details

Noga Amir
  • Weizmann Institute of Science, Rehovot, Israel
Oded Goldreich
  • Weizmann Institute of Science, Rehovot, Israel
Guy N. Rothblum
  • Apple, Cupertino, CA, USA

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Noga Amir, Oded Goldreich, and Guy N. Rothblum. Doubly Sub-Linear Interactive Proofs of Proximity. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.6

Abstract

We initiate a study of doubly-efficient interactive proofs of proximity, while focusing on properties that can be tested within query-complexity that is significantly sub-linear, and seeking interactive proofs of proximity in which  
1) The query-complexity of verification is significantly smaller than the query-complexity of testing. 
2) The query-complexity of the honest prover strategy is not much larger than the query-complexity of testing.  We call such proof systems doubly-sublinear IPPs (dsIPPs).
We present a few doubly-sublinear IPPs. A salient feature of these IPPs is that the honest prover does not employ an optimal strategy (i.e. a strategy that maximizes the verifier’s acceptance probability). In particular, the honest prover in our IPP for sets recognizable by constant-width read-once oblivious branching programs uses a distance-approximator for such sets.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
Keywords
  • Interactive Proof Systems
  • Interactive Proofs of Proximity
  • Query Complexity
  • Read Once Branching Programs
  • Sub-linear

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References

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