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Reports (Research Report) Year : 1993

On P completeness of some counting problems

Nadia Creignou
  • Function : Author
Miki Hermann


We prove that the counting problems #1-in-3Sat, #Not-All-Equal 3Sat and #3-Colorability, whose decision counterparts have been the most frequently used in proving NP-hardness of new decision problems, are #P-complete. On one hand, the explicit #P-completeness proof of #1-in-3Sat could be useful to prove complexity results within unification theory. On the ither hand, the fact that #3-Colorability is #P-complete allows us to deduce immediately that the enumerative versions of a large class of NP-complete problems are #P-complete. Moreover, our proofs shed some new light on the interest of exhibiting linear reductions between NP problems.
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Dates and versions

inria-00074528 , version 1 (24-05-2006)


  • HAL Id : inria-00074528 , version 1


Nadia Creignou, Miki Hermann. On P completeness of some counting problems. [Research Report] RR-2144, INRIA. 1993. ⟨inria-00074528⟩
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