computational complexity

, Volume 1, Issue 1, pp 3–40

Non-deterministic exponential time has two-prover interactive protocols

  • László Babai
  • Lance Fortnow
  • Carsten Lund

DOI: 10.1007/BF01200056

Cite this article as:
Babai, L., Fortnow, L. & Lund, C. Comput Complexity (1991) 1: 3. doi:10.1007/BF01200056


We determine the exact power of two-prover interactive proof systems introduced by Ben-Or, Goldwasser, Kilian, and Wigderson (1988). In this system, two all-powerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the inputx belongs to the languageL. We show that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time.

We also show that to prove membership in languages inEXP, the honest provers need the power ofEXP only.

The first part of the proof of the main result extends recent techniques of polynomial extrapolation used in the single prover case by Lund, Fortnow, Karloff, Nisan, and Shamir.

The second part is averification scheme for multilinearity of a function in several variables held by an oracle and can be viewed as an independent result onprogram verification. Its proof rests on combinatorial techniques employing a simple isoperimetric inequality for certain graphs:

Subject classifications


Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • László Babai
    • 1
    • 2
  • Lance Fortnow
    • 4
  • Carsten Lund
    • 3
  1. 1.University of ChicagoChicago
  2. 2.Eötvös UniversityBudapestHungary
  3. 3.Department of Computer ScienceUniversity of ChicagoChicago
  4. 4.Department of Computer ScienceUniversity of ChicagoChicago
  5. 5.DIMACSRutgers UniversityPiscataway