On P completeness of some counting problems

Abstract : 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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https://hal.inria.fr/inria-00074528
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Submitted on : Wednesday, May 24, 2006 - 3:40:58 PM
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Nadia Creignou, Miki Hermann. On P completeness of some counting problems. [Research Report] RR-2144, INRIA. 1993. ⟨inria-00074528⟩

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