IP = PSPACE using error-correcting codes

Research output: Contribution to journalArticlepeer-review


The IP Theorem, which asserts that IP = PSPACE [Lund et al., J. ACM, 39 (1992), pp. 859-868; Shamir, J. ACM, 39 (1992), pp. 878-880], is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The intuition that underlies the use of polynomials is commonly explained by the fact that polynomials constitute good errorcorrecting codes. However, the known proofs seem tailored to the use of polynomials and do not generalize to arbitrary error-correcting codes. In this work, we show that the IP theorem can be proved by using general error-correcting codes and their tensor products. We believe that this establishes a rigorous basis for the aforementioned intuition and sheds further light on the IP theorem.

Original languageEnglish
Pages (from-to)380-403
Number of pages24
JournalSIAM Journal on Computing
Issue number1
StatePublished - 2013
Externally publishedYes


  • Arithmetization
  • Error-correcting codes
  • Interactive proofs

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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