Abstract

The class of $# P$-complete problems is a class of computationally eqivalent counting problems (defined by the author in a previous paper) that are at least as difficult as the $NP$-complete problems. Here we show, for a large number of natural counting problems for which there was no previous indication of intractability, that they belong to this class. The technique used is that of polynomial time reduction with oracles via translations that are of algebraic or arithmetic nature.

Keywords

  1. counting
  2. enumeration
  3. reliability
  4. computational complexity
  5. NP-completeness
  6. permanent
  7. matchings

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cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 410 - 421
ISSN (online): 1095-7111

History

Submitted: 18 November 1977
Published online: 13 July 2006

Keywords

  1. counting
  2. enumeration
  3. reliability
  4. computational complexity
  5. NP-completeness
  6. permanent
  7. matchings

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