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Constraint Satisfaction Problems (CSPs) in Artificial Intelligence

Explore Constraint Satisfaction Problems (CSPs), a powerful problem-solving technique in AI. Learn how CSPs define problems with specific constraints and discover algorithms to find solutions that satisfy these restrictions. Understand the key components of a CSP and its applications in various AI domains.

Constraint Satisfaction Problems (CSPs) in Artificial Intelligence

Introduction

We've explored various AI problem-solving methods like adversarial and local search. These methods aim to find solutions, but without explicit constraints on the solution process. This section introduces constraint satisfaction, a different approach where solutions must meet specific conditions or rules.

What are Constraint Satisfaction Problems?

A constraint satisfaction problem (CSP) involves finding values for a set of variables that satisfy a set of constraints. CSPs are used when a problem requires variables to adhere to specific rules or limitations.

Components of a CSP

Three key components define a CSP:

  • Variables (X): A set of variables needing values assigned.
  • Domains (D): Each variable has a domain—a set of possible values it can take.
  • Constraints (C): Rules specifying allowable combinations of values for the variables.

In a CSP, the domains are the possible values for the variables given the problem's constraints. A constraint is defined by its scope (the variables involved) and its relation (the allowed combinations of values).

Solving Constraint Satisfaction Problems

To solve a CSP, we need to find an assignment of values to variables that satisfies all constraints. There are different types of assignments:

  • Consistent (Legal) Assignment: An assignment that satisfies all constraints.
  • Complete Assignment: An assignment where every variable has a value (a solution).
  • Partial Assignment: An assignment where only some variables have values.

Types of Domains and Constraints in CSPs

CSPs can involve different types of domains and constraints:

  • Discrete Domain: A finite or countably infinite set of values (e.g., integers from 1 to 9).
  • Continuous Domain: A continuous range of values (e.g., real numbers).
  • Unary Constraints: Restrict the value of a single variable.
  • Binary Constraints: Restrict the values of two variables.
  • Global Constraints: Involve more than two variables.

Different constraint types may require specific solution methods (e.g., linear programming for linear constraints, non-linear programming for non-linear constraints).

Example: Sudoku

Consider a Sudoku puzzle. The empty squares are the variables, the numbers 1-9 are the domain, and the rules (each number appears once in each row, column, and block) are the constraints. Solving the puzzle is a CSP.