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Efficient checking of computations

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STACS 90 (STACS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 415))

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Abstract

We show how to efficiently check computations using only logspace even if they are only given once. This result implies that a polynomial-time verifier can also be restricted to be logspace with essentially no loss in performance. We also use this result to show that every set in N P is equal to h(L) where h is a homomorphism and L is accepted by a one-way probabilistic logspace machine.

Work supported by DARPA and ONR contracts N00014-85-C-0456 and N00014-85-K-0465, and by NSF Cooperative Agreement DCR-8420948

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References

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

    Google Scholar 

  2. M. Blum, S. Kannan, Program Correctness Checking, Tech. Report TR-88-103, International Computer Science Institute, 1988.

    Google Scholar 

  3. A. Condon, Computational Models of Games, Ph.D. Thesis, Tech. Report 87-04-04, Computer Science Dept., University of Washington, Seattle, WA, 1987.

    Google Scholar 

  4. C. Dwork, L. Stockmeyer, Interactive Proof Systems with Finite State Verifiers, Tech. Report RJ 6262, IBM Research Division, Almaden Research Center, San Jose, CA, 1988.

    Google Scholar 

  5. S. Goldwasser, S. Micali, and C. Rackoff, The Knowledge Complexity of Interactive Proofs, Proc. of 17th STOC, 1985, ppp. 291–304.

    Google Scholar 

  6. M. Harrison, Introduction to Formal Language Theory, Addison-Wesley Publishing Company, 1978.

    Google Scholar 

  7. J. Hartmanis, N. Immerman, and S. Mahaney, One-Way Log-Tape Reductions, Proc. of 19th FOCS, 1978, pp. 65–72.

    Google Scholar 

  8. J. E. Hopcroft, W. J. Paul, and L. G. Valiant, On Time versus Space, JACM, 14 (1977), pp. 332–337.

    Article  Google Scholar 

  9. R. E. Ladner, The circuit value problem is logspace complete for P, SIGACT News, 7 (1975), pp. 18–20.

    Article  Google Scholar 

  10. R. J. Lipton, Fingerprinting Sets, CS-TR-212-89, Princeton University, 1989.

    Google Scholar 

  11. A. Schonhage, V. Strassen, Computing 7 (1971), pp. 281–292.

    Google Scholar 

  12. M. N. Wegman, J. L. Carter, New classes and applications of hash functions, 20th Annual Symposium on Foundations of Computer Science, (1979) 175–182.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Princeton University, USA

    Richard J. Lipton

Authors
  1. Richard J. Lipton
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Editor information

Christian Choffrut Thomas Lengauer

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© 1990 Springer-Verlag Berlin Heidelberg

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Lipton, R.J. (1990). Efficient checking of computations. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_44

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  • DOI: https://doi.org/10.1007/3-540-52282-4_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52282-9

  • Online ISBN: 978-3-540-46945-2

  • eBook Packages: Springer Book Archive

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