Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Theoretical Aspects of Computer Science

STACS 1991: STACS 91 pp 263–274Cite as

Interactive proof systems and alternating time-space complexity

  • Interactive Proof Systems
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

Abstract

We show a rough equivalence between alternating time-space complexity and a public-coin interactive proof system with the verifier having a polynomial related time-space complexity. Special cases include

  • All of NC has interactive proofs with a log-space polynomial-time public-coin verifier vastly improving the best previous lower bound of LOGCFL for this model [8].

  • All languages in P have interactive proofs with a polynomial-time public-coin verifier using o(log2 n) space.

  • All exponential-time languages have interactive proof systems with public-coin polynomial-space exponential-time verifiers.

Supported by NSF Grant CCR-9009936

Supported by a fellowship from the University of Århus.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Babai. Trading Group Theory for Randomness. In Proc. 17th STOC, pages 421–429, 1985.

    Google Scholar 

  2. L. Babai, L. Fortnow, and C. Lund. Non-deterministic Exponential Time has Two-Prover Interactive Protocols. In Proc. 31st FOCS, 1990.

    Google Scholar 

  3. L. Babai and S. Moran. Arthur-Merlin games: A Randomized Proof System, and a Hierarchy of Complexity Classes. JCSS, 36 2:254–276, 1988.

    Google Scholar 

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

    Google Scholar 

  5. A. Chandra, D. Kozen, and L. Stockmeyer. Alternation. JACM, 28 1:114–133, 1981.

    Article  Google Scholar 

  6. A. Condon. Space Bounded Probabilistic Game Automata. In Proc. 3rd Structure in Complexity Theory Conf., pages 162–174, 1988.

    Google Scholar 

  7. Stephen A. Cook. A Hierachy for Nondeterministic Time Complexity. Journal of Computer and System Science, 7:343–353, 1973.

    Google Scholar 

  8. L. Fortnow and M. Sipser. Interactive Proof Systems with a Log-Space Verifier. Manuscript. Later version appears in [16].

    Google Scholar 

  9. L. Fotnow and M. Sipser. Are There Interactive Protocols for co-NP Languages? Information Processing Letters, 28:249–251, 1988.

    Article  Google Scholar 

  10. L. Fortnow and M. Sipser. Probabilistic Computation and Linear Time. In 21st STOC, pages 148–156, 1989.

    Google Scholar 

  11. S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof-Systems. SIAM Journal on Computing, 18 1:186–208, 1989.

    Article  Google Scholar 

  12. S. Goldwasser and M. Sipser. Private Coins versus Public Coins in Interactive Proof Systems. In S. Micali, editor, Randomness and Computation, volume 5 of Advances in Computing Research, pages 73–90. JAI Press, 1989.

    Google Scholar 

  13. J. Hartmanis, P. M. Lewis II, and R. E. Stearns. Hierarchies of memory limited computations. In The 6th Annual IEEE Symp. on Switching Circuit Theory and Logical Design, pages 179–190, 1965.

    Google Scholar 

  14. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, Mass., 1979.

    Google Scholar 

  15. O. H. Ibarra. A note concerning nondeterministic tape complexities. J. ACM, 19 4:608–612, 1972.

    Article  Google Scholar 

  16. Fortnow L. Complexity-Theoretic Aspects of Interactive Proof Systems. PhD thesis, Massachusetts Institute of Technology, Laboratory for Computer Science, 1989. Tech Report MIT/LCS/TR-447.

    Google Scholar 

  17. C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic Methods for Interactive Proof Systems. In Proc. 31th IEEE Symp. on Foundations of Computer Science, 1990.

    Google Scholar 

  18. Wolfgang J. Paul, Ernest J. Prauß, and Rüdoger Reischuk. On Alternation. Acta Informatica, 14:243–255, 1980.

    Article  Google Scholar 

  19. G. Peterson and J. Reif. Multiple-person alternation. In Proc. 20th IEEE Symp. on Foundations of Computer Science, pages 348–363, 1979.

    Google Scholar 

  20. W. Ruzzo. On Uniform Circuit Complexity. JCSS, 22:365–381, 1981.

    Google Scholar 

  21. Schönhage, A. and V. Strassen. Schnelle Multiplikation grosser Zahlen. Computing, 7:281–292, 1971.

    Google Scholar 

  22. A. Shamir. IP=PSPACE. In Proc. 31st FOCS, 1990.

    Google Scholar 

  23. I. Sudborough. Time and Tape Bounded Auxiliary Pushdown Automata. Mathematical Foundations of Computer Science, pages 493–503, 1977.

    Google Scholar 

  24. I. Sudborough. On the Tape Complexity of Deterministic Context Free Languages. JACM, 25 3:405–414, 1978.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Chicago, USA

    Lance Fortnow & Carsten Lund

Authors
  1. Lance Fortnow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carsten Lund
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christian Choffrut Matthias Jantzen

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fortnow, L., Lund, C. (1991). Interactive proof systems and alternating time-space complexity. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020804

Download citation

  • DOI: https://doi.org/10.1007/BFb0020804

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation