Skip to main content
SpringerLink
Log in

Probabilistically Checkable Proofs and Applications

  • Conference paper
Book cover GISI 95

Part of the book series: Informatik aktuell ((INFORMAT))

  • 145 Accesses

Zusammenfassung

The question of what can be efficiently verified versus what can be efficiently computed has played a central role in complexity theory originating with the definition [C, L] of the class NP. With the discovery of fast randomized primality tests in the 70’s [SS, R] the definition of efficient computation has been largely extended to include randomized algorithms. In the 80’s, with the introduction of interactive proofs [GMR, Ba] much effort has been devoted to understanding how randomness enhances what can be efficiently verified.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Arora, C. Lund, S. Motwani, M. Sudan, M. Szegedi. Proof Verification and Intractability of Approximation Problems. In 33rd FOGS, pages 14–23, 1992.

    Google Scholar 

  2. S. Arora and S. Safra. Probabilistic Checkable Proofs: A New Characterization of NP. In 33rd FOGS, pages 1–13, 1992.

    Google Scholar 

  3. L. Babai. Trading Group Theory for Randomness. In 17th STOG, pages 421–420, 1985.

    Google Scholar 

  4. L. Babai, L. Fortnow, and C. Lund. Non-Deterministic Exponential Time has Two-Prover Interactive Protocols. In 31 st FOGS, pages 16–25, 1990.

    Google Scholar 

  5. L. Babai, L. Fortnow, L. Levin, and M. Szegedy. Checking Computations in Polylogarithmic Time. In 23rd STOG, pages 21–31, 1991.

    Google Scholar 

  6. L. Babai and S. Moran. Arthur-Merlin Garnes: A Randomized Proof System and a Hierarchy of Complexity Classes. JGSS, Vol. 36, pp. 254–276, 1988.

    MATH  MathSciNet  Google Scholar 

  7. M. Bellare and O. Goldreich. On Defining Proofs of Knowledge. In Crypto92.

    Google Scholar 

  8. Bellare and S. Goldwasser. The Complexity of Decision versus Search. SIAM Journal on Computing, Vol. 23, pages 97–119, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Bellare, S. Goldwasser, C. Lund and A. Russell. Efficient Probabilistically Checkable Proofs and Applications to Approximation. In 25th STOG, pages 294–304, 1993.

    Google Scholar 

  10. M. Ben-Or, O. Goldreich, S. Goldwasser, J. hastad, J. Kilian, S. Micali and P. Rogaway. Everything Provable is Provable in Zero-Knowledge. In Grypto88, Springer Verlag, LNCS Vol. 403, pages 37–56, 1990

    Google Scholar 

  11. M. Ben-Or, S. Goldwasser, J. Kilian and A. Wigderson. Multi-Prover Interactive Proofs: How to Remove Intractability Assumptions. In 20th STOG, pages 113–131, 1988.

    Google Scholar 

  12. M. Blum, M. Luby and R. Rubinfeld. Self-Testing/Correcting with Applications to Numerical Problems. In 22nd STOG, 1990.

    Google Scholar 

  13. G. Brassard, D. Chaum and C. Crépeau. Minimum Disclosure Proofs of Knowledge. JGSS, pages 156–189, 1988. Extended abstract, by Brassard and Crépeau, in 27th FOGS, 1986.

    Google Scholar 

  14. R. B. Boppana and M. M. Halldórsson, Approximating maximum independent sets by excluding subgraphs, in the Proc. of 2nd Scand. Workshop on Algorithm Theory, Springer-Verlag Lecture Notes in Computer Science 447, pp. 13–25, July, 1990.

    Google Scholar 

  15. M. Ben-Or, T. Rabin. Verifiable Secret Sharing and Multiparty Protocols with Honest Majority, 21st STOC.

    Google Scholar 

  16. M. Ben-Or, S. Goldwasser, A. Wigderson. Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation, Proc. of 20th STOC (1988), 1–10.

    Google Scholar 

  17. Bellare, M., Goldreich, O., and Sudan, M., Reductions, Codes, PCP’s, and Inapproximability, preprint.

    Google Scholar 

  18. L. Babai, L. Fortnow and C. Lund. Non-Deterministic Exponential Time has Two-Prover Interactive Protocols. FOCS 90.

    Google Scholar 

  19. M. Bellare. Interactive Proofs and Approximation. IBM Research Report RC 17969 (May 1992).

    Google Scholar 

  20. M. Bellare and P. Rogaway. The Complexity of Approximating a Nonlinear program. IBM Research Report RC 17831 (March 1992).

    Google Scholar 

  21. S. Cook, The Complexity of Theorem-Proving Procedures, Proceeding of 3rd Symposium of Theory of Computation, (1971), pp. 151–158.

    Google Scholar 

  22. U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy. Approximating Clique is almost NP-complete. In 32nd FOGS, pages 2–12, 1991.

    Google Scholar 

  23. U. Feige, D. Lapidot, and A. Shamir. Multiple non-interactive zero knowledge proofs based on a single random string. In 31st FOGS, pages 308–317, 1990.

    Google Scholar 

  24. L. Fortnow, J. Rompel and M. Sipser. On the Power of Multi-Prover Interactive Protocols. In Proc. 3rd IEEE Symp. on Structure in Gomplexity Theory, pages 156–161, 1988.

    Google Scholar 

  25. U. Feige, A. Fiat and A. Shamir, Zero Knowledge Proofs of Identity, 19th ACM Symp. on Theory of Computing, pp. 210–217, 1987.

    Google Scholar 

  26. Feige U., Private Communication.

    Google Scholar 

  27. U. Feige and L. Lovász. Two-Prover One Round Proof Systems: Their Power and their Problems. STOC 92.

    Google Scholar 

  28. M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979.

    MATH  Google Scholar 

  29. O. Goldreich, S. Micali and A. Wigderson. Proofs that Yield Nothing but their Validity or All Languages in NP Have Zero-Knowledge Proof Systems. JACM, Vol. 38, No.1, pages 691–729, 1991. Extended abstract in 27th FOGS, 1986.

    MATH  MathSciNet  Google Scholar 

  30. O. Goldreich, R. Ostrovsky and E. Petrank. Knowledge Complexity and Computational Complexity. In 26th STOG, 1994.

    Google Scholar 

  31. O. Goldreich and E. Petrank. Quantifying Knowledge Complexity. In 32nd FOGS, pp. 59–68, 1991.

    Google Scholar 

  32. S. Goldwasser, S. Micali and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM Journal on Gomputing, Vol. 18, pages 186–208, 1989. Extended abstract in 17th STOG, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  33. S. Goldwasser and M. Sipser. Private Coins versus Public Coins in Interactive Proof Systems. In 18th STOG, pages 59–68, 1986.

    Google Scholar 

  34. R. Impagliazzo and M. Yung. Direct Zero-Knowledge Computations. In Grypt087, Springer Verlag, LNCS Vol. 293, pages 40–51, 1987.

    Google Scholar 

  35. Richard M. Karp, Reducibility Among Combinatorial Problems, in the book ”Complexity of Computer Computations”, Plenum Press, publ. Raymond E. Miller and James W. Thatcher, pp. 85–103, 1972.

    Google Scholar 

  36. C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic Methods for Interactive Proof Systems. In 31st FOGS, pages 2–10, 1990.

    Google Scholar 

  37. C. Lund and M. Yannakakis. On the Hardness of Approximate Minimization Problems, In 25th STOG, pages 286–293, 1993.

    Google Scholar 

  38. Levin, L., Universal’nyĭe perebornyĭe zadachi (Universal search problems: in Russian), ”Problemy Peredachi Informatsii”, v. 9, No.3, pp. 265–266.

    Google Scholar 

  39. C. H. Papadimitriou and M. Yannakakis. Optimization, Approximation, and Complexity Classes. In 20th STOG, pages 229–234, 1988.

    Google Scholar 

  40. Rabin, M., Probabilistic Algorithms for testing primality, J. of Num. Th. 12, 128–138 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  41. Solovay and Strassen, A fast Monte-Carlo test for Primality, SIAM. J. of Compo 6 (1977).

    Google Scholar 

  42. A. Shamir. IP=PSPACE. In 31st FOeS, pages 11–15, 1990.

    Google Scholar 

  43. D. Zuckerman. NP-Complete Problems have a version that is hard to Approximate. Manuscript (June 1, 1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachussetts Institute of Technology, USA

    Shafi Goldwasser

  2. Weizmann Institute, Israel

    Shafi Goldwasser

Authors
  1. Shafi Goldwasser
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Informatik, ETH Zentrum, CH-8092, Zürich, Switzerland

    Friedbert Huber-Wäschle  & Peter Widmayer  & 

  2. Institut für Informatik, Universität Zürich, Winterthurer Strasse 190, CH-8057, Zürich, Switzerland

    Helmut Schauer

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goldwasser, S. (1995). Probabilistically Checkable Proofs and Applications. In: Huber-Wäschle, F., Schauer, H., Widmayer, P. (eds) GISI 95. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79958-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-79958-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60213-2

  • Online ISBN: 978-3-642-79958-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation