Problem Decomposition: Goal Trees, Rule Based Systems, Rule Based Expert Systems. Planning: STRIPS, Forward and Backward State Space Planning, Goal Stack Planning, Plan Space Planning, A Unified Framework For Planning. Constraint Satisfaction : N-Queens, Constraint Propagation, Scene Labeling, Higher order and Directional Consistencies, Backtracking and Look ahead Strategies.

1. Topic To Be Covered:
Constraint Satisfaction Problem(Approach)
In AI
Jagdamba Education Society's
SND College of Engineering & Research Centre
Department of Computer Engineering
SUBJECT: Artificial Intelligence & Robotics
Lecture No-09(UNIT-02)
Prof.Dhakane Vikas N

2. Constraint Satisfaction Problem In AI
What is CSP????
 In artificial intelligence and operations research, constraint satisfaction is
the process of finding a solution to a problem by satisfying set of
constraints.
 It is heuristic based Technique.
 CSP is also called as decision problem.

3. Constraint Satisfaction Problem In AI
What is CSP????
 Way of representation of problem in CSP is different from state space
representation
 Some popular example of Constraint satisfaction problem are like Map
(Graph) Coloring problem-N-Queens Problem & Sudoku etc.

4. Constraint Satisfaction Problem In AI
What is CSP????
 For Example-01(Sudoku):
 Sudoku is played on a grid of 9 x 9 spaces.
 Within the rows and columns are 9
“squares” (made up of 3 x 3 spaces).
 Each row, column and square (9 spaces
each) needs to be filled out with the
numbers 1-9, without repeating any
numbers within the row, column or
square.
 As you can see from the image below of an
actual Sudoku grid, each Sudoku grid
comes with a few spaces already filled in;
 the more spaces filled in, the easier the
game – the more difficult Sudoku puzzles
have very few spaces that are already
filled in.

5. Constraint Satisfaction Problem In AI
What is CSP????
Following are main Components of CSP
 CSP consist of three
Components:(V,D,C)
1)V is the set of finite variables
{V1,V2,V3…Vn }
-In given Sudoku example, available
spaces where we have to make entry of
data(value) is called as VARIABLES….
2)D is the set of Domains
{D1,D2,D3..Dn} one for each variable.
-Here in given Sudoku example
domains are values(1-9) that has to be
placed in certain variables.

6. Constraint Satisfaction Problem In AI
What is CSP????
Following are main Components of CSP
 CSP consist of three Components:(V,D,C)
3) C is the set of Constraints(Rules) that
specify allowable combinations of
values.(C1,C2,C3)
-Which value to place in which variable by
selecting it from its domain is based on set of
constraints.
-For given Sudoku example Constraints are as
follows:
a)Use value from 1-9
b)No repetition of values on same row,
column & square box.

7. Constraint Satisfaction Problem In AI

8. Constraint Satisfaction Problem In AI
What is CSP????
 For Example-02(GCP):Graph Coloring Problem
 For Example(GCP):Vertex coloring is the most common graph coloring
problem. The problem is, given m colors, find a way of coloring the
vertices of a graph such that no two adjacent vertices are colored using
same color. (m=3 & node=10)

9. Constraint Satisfaction Problem In AI
What is CSP????
 For Example-03(N-queens Problem)
 This problem is to find an arrangement of N queens on a chess board,
such that no queen can attack any other queens on the board.
 The N Queen is the problem of placing N chess queens on an N×N
chessboard so that no two queens attack each other.
 Queen can attack each other if they are in same column, row & diagonal.
 Example:-04 queen