On the interactive complexity of graph reliability

  • Jean-Marc Couveignes
  • Juan Francisco Diaz-Frias
  • Michel de Rougemont
  • Miklos Santha
Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 880)


We give an interactive protocol for s — t RELIABILITY, the well known reliability problem on graphs. Our protocol shows that if IP(f(n)) denotes the class of languages whose interactive complexity is O(f(n)), that is the set of languages which can be accepted by an interactive proof system with O(f(n)) number of rounds, then s — t RELIABILITY ε IP(n). This complexity is significantly smaller than what one could get via reduction to QBF, the standard PSPACE-complete language. Another interesting aspect of our protocol is that it includes a general method to deal with rational numbers in interactive proof systems.


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  1. [1]
    L. Babai (1985), Trading group theory for randomness, Proceedings of 17th ACM STOC, 421–429.Google Scholar
  2. [2]
    L. Babai and L. Fortnow (1990), A characterization of #P by arithmetic straight line programs, Proceedings of 31st IEEE FOCS, 26–34.Google Scholar
  3. [3]
    L. Babai and S. Moran (1988), Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes, Journal of Computer and System Sciences 36, 254–276.Google Scholar
  4. [4]
    R. Boppana, J. Hastad and S. Zachos (1987), Does co — NP have short interactive proofs?, Information Processing Letters 25, 127–132.Google Scholar
  5. [5]
    J. Diaz-Frias and M. de Rougemont (1992), A theory of robust planning, Proceedings of IEEE International Conference on Robotics and Automation, 2453–2459.Google Scholar
  6. [6]
    S. Goldwasser, S. Micali and C. Rackoff (1989), The knowledge complexity of interactive proof systems, SIAM Journal of Computing, 18: 1, 186–208.Google Scholar
  7. [7]
    C. Lund, L. Fortnow, H. Karloff and N. Nisan (1990), Algebraic methods for interactive proof systems, Proceedings of 31st IEEE FOCS, 2–10.Google Scholar
  8. [8]
    A. Shamir (1990), IP = PSPACE, Proceedings of 31st IEEE FOCS, 11–15.Google Scholar
  9. [9]
    L. Valiant (1979), The complexity of enumeration and reliability problems, SIAM Journal of Computing, 8: 3, 410–421.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jean-Marc Couveignes
    • 1
  • Juan Francisco Diaz-Frias
    • 2
  • Michel de Rougemont
    • 3
    • 4
  • Miklos Santha
    • 5
  1. 1.ENS, LIENSParisFrance
  2. 2.Dept, Giencias de la ComputacionUniversidad del ValleCaliColombia
  3. 3.CNRSUniversite Paris-Sud, LRIOrsay
  4. 4.Ecole Nationale Supérieure de Techniques AvancéesFrance
  5. 5.CNRSUniversité Paris-Sud, LRIOrsayFrance

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