Constraint Satisfaction Problem
Constraint satisfaction problems (CSPs) are mathematical problems defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of intense 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 unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. The boolean satisfiability problem (SAT), the Satisfiability Modulo Theories (SMT) and answer set programming (ASP) can be roughly thought of as certain forms of the constraint satisfaction problem.
Examples of simple problems that can be modeled as a constraint satisfaction problem
- Eight queens puzzle
- Map coloring problem
- Sudoku
Examples demonstrating the above are often provided with tutorials of ASP, boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems.
Read more about Constraint Satisfaction Problem: Formal Definition, Resolution of CSPs, Variants of CSPs
Famous quotes containing the words constraint, satisfaction and/or problem:
“In America a woman loses her independence for ever in the bonds of matrimony. While there is less constraint on girls there than anywhere else, a wife submits to stricter obligations. For the former, her father’s house is a home of freedom and pleasure; for the latter, her husband’s is almost a cloister.”
—Alexis de Tocqueville (1805–1859)
“... we have the satisfaction of knowing that because all of us believed, we inspired, motivated, and liberated some of the most beautiful people on earth—young, gifted, and black.”
—Mary Allison Burch (b. 1906)
“The family environment in which your children are growing up is different from that in which you grew up. The decisions our parents made and the strategies they used were developed in a different context from what we face today, even if the “content” of the problem is the same. It is a mistake to think that our own experience as children and adolescents will give us all we need to help our children. The rules of the game have changed.”
—Lawrence Kutner (20th century)