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Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation pp 333–372Cite as

Short Locally Testable Codes and Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6650))

Abstract

We survey known results regarding locally testable codes and locally testable proofs (known as PCPs), with emphasis on the length of these constructs. Local testability refers to approximately testing large objects based on a very small number of probes, each retrieving a single bit in the representation of the object. This yields super-fast approximate-testing of the corresponding property (i.e., be a codeword or a valid proof). We also review the related concept of local decodable codes.

The survey consists of two independent (i.e., self-contained) parts that cover the same material at different levels of rigor and detail. Still, in spite of the repetitions, there may be a benefit in reading both parts.

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Authors
  1. Oded Goldreich
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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, 76100, Rehovot, Israel

    Oded Goldreich

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Goldreich, O. (2011). Short Locally Testable Codes and Proofs. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_25

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  • DOI: https://doi.org/10.1007/978-3-642-22670-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22669-4

  • Online ISBN: 978-3-642-22670-0

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