Round Complexity Versus Randomness Complexity in Interactive Proofs

Author Maya Leshkowitz



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Maya Leshkowitz
  • Weizmann Institute of Science, Rehovot, Israel

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Maya Leshkowitz. Round Complexity Versus Randomness Complexity in Interactive Proofs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.49

Abstract

Consider an interactive proof system for some set S that has randomness complexity r(n) for instances of length n, and arbitrary round complexity. We show a public-coin interactive proof system for S of round complexity O(r(n)/log n). Furthermore, the randomness complexity is preserved up to a constant factor, and the resulting interactive proof system has perfect completeness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
Keywords
  • Interactive Proofs

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References

  1. Laszlo Babai. Trading group theory for randomness. In ACM Symposium on the Theory of Computing, pages 421-429, 1985. Google Scholar
  2. Laszlo Babai and Shlomo Moran. Arthur-merlin games: A randomized proof system and a hierarchy of complexity classes. Journal of Computer and System Science, 36:254-276, 1988. Google Scholar
  3. Mihir Bellare, Oded Goldreich, and Shafi Goldwasser. Randomness in interactive proofs. Computational Complexity, 3:319-354, 1993. Google Scholar
  4. Martin Fürer, Oded Goldreich, Yishay Mansour, Michael Sipser, and Stathis Zachos. On completeness and soundness in interactive proof systems. Advances in Computing Research, 5:429-442, 1989. Google Scholar
  5. Oded Goldreich and Maya Leshkowitz. On emulating interactive proofs with public coins. Electronic Colloquium on Computational Complexity (ECCC), 23:66, 2016. Google Scholar
  6. Oded Goldreich, Silvio Micali, and Avi Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. Journal of the ACM, 38(3):691-729, 1991. Preliminary version in 27th FOCS, 1986. Google Scholar
  7. Oded Goldreich, Salil P. Vadhan, and Avi Wigderson. On interactive proofs with a laconic prover. Computational Complexity, 11(1-2):1-53, 2002. Google Scholar
  8. Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof systems. SIAM Journal on Computing, 18(1):186-208, 1989. Preliminary version in 17th STOC, 1985. Earlier versions date to 1982. Google Scholar
  9. Shafi Goldwasser and Michael Sipser. Private coins versus public coins in interactive proof systems. Advances in Computing Research, 5:73-90, 1989. Extended abstract in 18th STOC, 1986. Google Scholar
  10. Adam R. Klivans and Dieter van Melkebeek. Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. SIAM Journal on Computing, 31(5):1501-1526, 2002. Google Scholar
  11. Maya Leshkowitz. Round complexity versus randomness complexity in interactive proofs. Electronic Colloquium on Computational Complexity (ECCC), 24:55, 2017. Full version of the paper. Google Scholar
  12. Carsten Lund, Lance Fortnow, Howard J. Karloff, and Noam Nisan. Algebraic methods for interactive proof systems. Journal of the ACM, 39(4):859-868, 1992. Extended abstract in 31st FOCS, 1990. Google Scholar
  13. Ronen Shaltiel and Christopher Umans. Low-end uniform hardness versus randomness tradeoffs for AM. SIAM Journal on Computing, 39(3):1006-1037, 2009. Google Scholar
  14. Adi Shamir. IP = PSPACE. Journal of the ACM, 39(4):869-877, 1992. Preliminary version in 31st FOCS, 1990. Google Scholar
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