# Constraint satisfaction

**constraintsconstraintconstraint satisfaction problemsconstraint programmingconstraint-basedsatisfaction of constraints**

In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy.wikipedia

107 Related Articles

### Constraint satisfaction problem

**constraint solvingconstraint satisfactionconstraint satisfaction problems**

Often used are constraints on a finite domain, to the point that constraint satisfaction problems are typically identified with problems based on constraints on a finite domain.

CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods.

### Local consistency

**constraint propagationarc consistencybucket elimination**

Constraint propagation are other methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always. The most used techniques are variants of backtracking, constraint propagation, and local search.

In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints.

### Local search (constraint satisfaction)

**local searchlocal search algorithm**

Such problems are usually solved via search, in particular a form of backtracking or local search.

In constraint satisfaction, local search is an incomplete method for finding a solution to a problem.

### Search algorithm

**searchsearchingkeyword search**

Such problems are usually solved via search, in particular a form of backtracking or local search.

### Constraint logic programming

**CLPConstraint logicConstraint Programming**

The constraints in the goal and in the clauses used to prove the goal are accumulated into a set called constraint store.

Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction.

### Local search (optimization)

**local searchlocal optimizationlocal search algorithm**

The most used techniques are variants of backtracking, constraint propagation, and local search.

### Satisfiability

**satisfiablesatisfiability problemsatisfies**

In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy.

### Interval propagation

**Interval Constraint Propagationbounded-error estimation**

Problems that can be expressed as constraint satisfaction problems are the eight queens puzzle, the Sudoku solving problem and many other logic puzzles, the Boolean satisfiability problem, scheduling problems, bounded-error estimation problems and various problems on graphs such as the graph coloring problem.

Interval propagation considers an estimation problem as a constraint satisfaction problem.

### Mathematical optimization

**optimizationmathematical programmingoptimal**

These are typically solved as optimization problems in which the optimized function is the number of violated constraints.

### Prolog

**SICStus PrologProlog IISICStus**

Languages often used for constraint programming are Prolog and C++.

Constraint logic programming extends Prolog to include concepts from constraint satisfaction.

### Comet (programming language)

**Comet**

It offers a range of optimization algorithms: from mathematical programming to constraint programming, local search algorithm and "dynamic stochastic combinatorial optimization."

### Feasible region

**candidate solutionfeasible setsearch space**

A solution is therefore a set of values for the variables that satisfies all constraints—that is, a point in the feasible region.

Constraint satisfaction is the process of finding a point in the feasible region.

### Knowledge-based configuration

**configuration systemproduct configuratorconfigurable products**

### Artificial intelligence

**AIA.I.artificially intelligent**

In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy.

### Operations research

**operational researchoperation researchoperational analysis**

In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy.

### Constraint (mathematics)

**constraintconstraintsconstrained**

### Variable (mathematics)

**variablesvariableunknown**

### Backtracking

**backtracking searchbacktracksbacktrack**

Such problems are usually solved via search, in particular a form of backtracking or local search. The most used techniques are variants of backtracking, constraint propagation, and local search.

### Variable elimination

Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm.

### Simplex algorithm

**simplex methodSimplexalgorithms**

Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm.

### Programming language

**programming languageslanguagedialect**

During the 1980s and 1990s, embedding of constraints into a programming language were developed.

### Constraint programming

**constraintconstraint solverconstraint programming language**

Languages often used for constraint programming are Prolog and C++.

### C++

**C++ programming languageC++98C with Classes**

Languages often used for constraint programming are Prolog and C++.

### Eight queens puzzle

**n''-queens problemn-Queens Problemn queens problem**

Problems that can be expressed as constraint satisfaction problems are the eight queens puzzle, the Sudoku solving problem and many other logic puzzles, the Boolean satisfiability problem, scheduling problems, bounded-error estimation problems and various problems on graphs such as the graph coloring problem.

### Sudoku

**wordokuGNOME SudokuPlatinum Sudoku**

Problems that can be expressed as constraint satisfaction problems are the eight queens puzzle, the Sudoku solving problem and many other logic puzzles, the Boolean satisfiability problem, scheduling problems, bounded-error estimation problems and various problems on graphs such as the graph coloring problem.