'''Constraint satisfaction problems''' ('''CSPs''') are mathematical questions defined as thea set of objects whose [[State (computer science)|state]] must satisfy a number of [[Constraint (mathematics)|constraints]] or/ [[Limit (mathematics)|limitations]]. CSPs represent athe entities in a problem as a homogeneous collection of finite constraints over [[Variable (mathematics)|variable]]s, which is solved by [[constraint satisfaction]] methods. CSPs are the subject of research in both [[artificial intelligence]] and [[operations research]], since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. [[Complexity of constraint satisfaction|CSPs often exhibit high complexity]], requiring a combination of [[heuristics]] and [[combinatorial search]] methods to be solved in a reasonable time. [[Constraint programming]] (CP) is the field of research that specifically focuses on tackling these kinds of problems.<ref>{{Cite book|title=Constraint Networks: Techniques and Algorithms|last=Lecoutre|first=Christophe|publisher=Wiley|year=2013|isbn=978-1-118-61791-5|pages=26}}</ref><ref>{{Cite web|url=http://www.springer.com/computer/ai/journal/10601|title=Constraints – incl. option to publish open access|website=springer.com|language=en|access-date=2019-10-03}}</ref> Additionally, [[Boolean satisfiability problem]] (SAT), the [[satisfiability modulo theories]] (SMT), [[mixed integer programming]] (MIP) and [[answer set programming]] (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
Examples of problems that can be modeled as a constraint satisfaction problem include:
