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Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

Authors Alessandro Chiesa, Peter Manohar, Igor Shinkar



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Author Details

Alessandro Chiesa
  • UC Berkeley, Berkeley, CA, USA
Peter Manohar
  • UC Berkeley, Berkeley, CA, USA
Igor Shinkar
  • Simon Fraser University, Vancouver, Canada

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Alessandro Chiesa, Peter Manohar, and Igor Shinkar. Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 25:1-25:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITCS.2019.25

Abstract

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proofs (PCPs) that are sound against non-signaling strategies. In this paper we prove that the exponential-length constant-query PCP construction due to Arora et al. (JACM 1998) is sound against non-signaling strategies. Our result offers a new length-vs-query tradeoff when compared to the non-signaling PCP of Kalai, Raz, and Rothblum (STOC 2013 and 2014) and, moreover, may serve as an intermediate step to a proof of a non-signaling analogue of the PCP Theorem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • probabilistically checkable proofs
  • linearity testing
  • non-signaling strategies

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