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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)

Abstract

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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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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