Editing Constraint satisfaction problem (section)

===Function problems===
A similar situation exists between the functional classes [[FP (complexity)|FP]] and [[Sharp-P|#P]]. By a generalization of [[Ladner's theorem]], there are also problems in neither FP nor [[Sharp-P-complete|#P-complete]] as long as FP ≠ #P. As in the decision case, a problem in the #CSP is defined by a set of relations. Each problem takes a [[Boolean logic|Boolean]] formula as input and the task is to compute the number of satisfying assignments. This can be further generalized by using larger domain sizes and attaching a weight to each satisfying assignment and computing the sum of these weights. It is known that any complex weighted #CSP problem is either in FP or #P-hard.<ref>{{Cite conference| last1 = Cai | first1 = Jin-Yi| last2 = Chen | first2 = Xi| doi = 10.1145/2213977.2214059 | title = Complexity of counting CSP with complex weights | book-title = [[Symposium on Theory of Computing|Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing (STOC '12)]] | pages = 909–920 | year = 2012 | isbn = 978-1-4503-1245-5| arxiv        = 1111.2384| s2cid = 53245129}}</ref>