Short locally testable codes and proofs: a survey in two parts

Authors:
Oded Goldreich
Affiliations:
Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel
Venue:
Property testing
Year:
2010

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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 approximatetesting 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.