# Defining Constraint Satisfaction Problems¶

Constraint satisfaction problems require that all a problem’s variables be assigned values, out of a finite domain, that result in the satisfying of all constraints. The ConstraintSatisfactionProblem class aggregates all constraints and variables defined for a problem and provides functionality to assist in problem solution, such as verifying whether a candidate solution satisfies the constraints.

## Class¶

class ConstraintSatisfactionProblem(vartype)[source]

A constraint satisfaction problem.

Parameters: vartype (Vartype/str/set) – Variable type for the binary quadratic model. Supported values are: SPIN, 'SPIN', {-1, 1} BINARY, 'BINARY', {0, 1}
constraints

Constraints that together constitute the constraint satisfaction problem. Valid solutions satisfy all of the constraints.

Type: list[Constraint]
variables

Variables of the constraint satisfaction problem as a dict, where keys are the variables and values a list of all of constraints associated with the variable.

Type: dict[variable, list[Constraint]]
vartype

Enumeration of valid variable types. Supported values are SPIN or BINARY. If vartype is SPIN, variables can be assigned -1 or 1; if BINARY, variables can be assigned 0 or 1.

Example

This example creates a binary-valued constraint satisfaction problem, adds two constraints, $$a = b$$ and $$b \ne c$$, and tests $$a,b,c = 1,1,0$$.

>>> import operator
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem('BINARY')
>>> csp.check({'a': 1, 'b': 1, 'c': 0})
True


## Methods¶

 ConstraintSatisfactionProblem.add_constraint(…) Add a constraint. ConstraintSatisfactionProblem.add_variable(v) Add a variable.
 ConstraintSatisfactionProblem.check(solution) Check that a solution satisfies all of the constraints.
 ConstraintSatisfactionProblem.fix_variable(v, …) Fix the value of a variable and remove it from the constraint satisfaction problem.