Constraint Satisfaction Problem

We can break down a Constraint Satisfaction Problem (CSP) into:

• a finite set of variables $X\{x^1\dots x^n\}$ defines all elements that need to be given a value in the problem
• a set of domains $D\{D^1\dots D^i\}$ defines what possible values can be assigned to each variable $[v^1\dots v^j]$
• a set of constraints $C\{C^1\dots C^k\}$ rules that dictate a relation between variables in $X$ each constraint $C^i$ is a pairing of scope and relation

A CSP solution is an instance of all variables in $X$ using vales in $D$ that satisfies all constraints in $C$.