On the Hardness of Permanent

  • Jin-Yi Cai
  • A. Pavan
  • D. Sivakumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)


We prove that if there is a polynomial time algorithm which computes the permanent of a matrix of order n for any inverse polynomial fraction of all inputs, then there is a BPP algorithm computing the permanent for every matrix. It follows that this hypothesis implies P#p = BPP. Our algorithm works over any sufficiently large finite field (polynomially larger than the inverse of the assumed success ratio), or any interval of integers of similar range. The assumed algorithm can also be a probabilistic polynomial time algorithm. Our result is essentially the best possible based on any black box assumption of permanent solvers, and is a simultaneous improvement of the results of Gemmell and Sudan [GS92], Feige and Lund [FL92] as well as Cai and Hemachandra [CH91], and Toda (see [ABG90]).


Success Probability Polynomial Time Algorithm Success Ratio Permanent Function Bernoulli Trial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jin-Yi Cai
    • 1
  • A. Pavan
    • 1
  • D. Sivakumar
    • 2
  1. 1.Department of Computer Science and EngineeringState University of New York at BuffaloBuffalo
  2. 2.Department of Computer ScienceUniversity of HoustonHouston

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