How does arc consistency work in constraint satisfaction problems?

Can you explain what arc consistency means in constraint satisfaction problems?

Arc consistency is a property of a binary constraint satisfaction problem where for every value of a variable, there exists a consistent value in the connected variable.

How do you check if a variable is arc consistent?

To check if a variable is arc consistent, you examine each value of the variable and see if there is at least one value in the connected variable that satisfies the constraints.

Can you give me an example of arc consistency in action?

Sure! If you have variables A and B with values {1, 2} and {2, 3} respectively, and a constraint that A < B, then A=1 is arc consistent because B can be 2 or 3.

What happens if a variable is not arc consistent?

If a variable is not arc consistent, it means that some values cannot be satisfied by any values of the connected variable, which may lead to a failure in finding a solution.