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A binary constraint, in constraint satisfaction problems (CSPs), refers to a constraint that involves exactly two variables. Unlike unary constraints, which apply to a single variable, binary constraints are relationships or conditions that must be satisfied between pairs of variables in a CSP. 

In mathematical terms, a binary constraint typically defines restrictions on the joint values that two variables can take simultaneously. The goal is to find assignments of values to variables that satisfy all binary constraints in the problem. 

For instance, consider a CSP involving three variables representing different tasks (A, B, and C), and there is a binary constraint between A and B, specifying that A must be performed before B. This constraint could be expressed as: 

Binary Constraint: A must precede B. 

In this example, the binary constraint restricts the possible combinations of values for variables A and B, ensuring that the assignment is consistent with the requirement that task A must be completed before task B. 

Binary constraints play a crucial role in modeling relationships between variables in CSPs, representing dependencies or interactions that must be considered during the search for a valid solution. The relationships specified by binary constraints contribute to the overall set of conditions that define a feasible solution to the CSP. 

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