The correct answer is: C. NP hard
A constraint satisfaction problem (CSP) is a problem in which a set of variables must be assigned values from a finite domain such that a set of constraints are satisfied. CSPs are often used to model real-world problems such as scheduling, planning, and diagnosis.
A problem is NP-complete if it is both NP-hard and in NP. NP-hard problems are the hardest problems in NP, in the sense that any problem in NP can be reduced to an NP-hard problem in polynomial time.
A problem is NP-hard if it is at least as hard as any problem in NP. This means that if there is an efficient algorithm for solving an NP-hard problem, then there is also an efficient algorithm for solving any problem in NP.
The domain size of a CSP is the number of possible values that each variable can take. The complexity of solving a CSP depends on the domain size. For small domain sizes, CSPs can be solved efficiently using backtracking or local search algorithms. However, for large domain sizes, CSPs are typically NP-hard and cannot be solved efficiently.
In conclusion, solving a constraint satisfaction problem on a finite domain is an NP-hard problem with respect to the domain size. This means that there is no known efficient algorithm for solving CSPs on large domains.