#P-completeness
Statement
#P is the class of counting problems: given an NP machine, count the number of accepting paths. Valiant (1979) proved that computing the permanent of a 0-1 matrix is #P-complete—the axiomatic definition of counting complexity. Knuth (1997), Turing (2010).
Formula
#P-complete: Permanent
Proof sketch
ZFC 9+1 → Turing machines, Boolean circuits. Permanent encodes number of perfect matchings. Reduction from #SAT. Counting complexity axiomatized.
Source
Valiant, SIAM J. Comput. 8 (1979). Knuth Prize 1997, Turing Award 2010.
Domains
computer-science