NPTEL Artificial Intelligence : Search Methods For Problem solving Week 12 Assignment Answers 2024

1. To model a problem as a CSP one has to

choose a set of variables and a domain for each variable
explicitly specify the constraints between some variables
always explicitly specify the constraints between all variables
study the history of the problem and its solutions

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2. A constraint on a subset of the variables

expresses the fact that the variables must participate in a solution to the CSP
expresses the fact that the values that the variables can take are interdependent
expresses all combinations of values that the variables can take
expresses all combinations of values that are part of some solution

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3. Which of the following statements are true regarding solving a CSP

Values must be assigned to ALL variables such that ALL constraints are satisfied
Values must be assigned to at least SOME variables such that ALL constraints are satisfied
Values must be assigned to ALL variables such that at least SOME constraints are satisfied
Values must be assigned to at least SOME variables such that at least SOME constraints are satisfied

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4. While modeling components for the task of model based diagnosis, each component is modeled as

a physical device and the material it is made of
a physical device and the conditions under which it works correctly
a constraint that captures the relation between its inputs and outputs

Answer :-

5. The goal of constraint propagation or consistency enforcement is

to extend the existing constraints to newer variables in the network
to distribute the constraints more evenly amongst the variables
to ensure that the CSP has a solution
to modify the constraint network to prune the space explored by the search algorithm

Answer :-

END GROUP 1

BEGIN GROUP 2

Consider a CSP with three variables X, Y and Z, where DX = DY = DZ = {1,2,…,9} and two constraints:

R XY : 2X = Y,
R YZ : YZ = 16.

Use matching-diagram where necessary.

6. For the above CSP, the value of DX after the network is made arc consistent is _________ .

Enter a comma separated list of domain values in ascending order.
Enter NIL if the domain is empty.
Answer format: 1,2,3,4

Answer :-

7. For the above CSP the value of DY after the network is made arc consistent is ____________ .

Enter a comma separated list of domain values in ascending order.
Enter NIL if the domain is empty.
Answer format: 1,2,3,4

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8. For the above CSP the value of DZ after the network is made arc consistent is _______________ .

Enter a comma separated list of domain values in ascending order.
Enter NIL if the domain is empty.
Answer format: 1,2,3,4

Answer :-

9. Solve the CSP. Enter a solution in the textbox, enter the values of X, Y, Z in that order.

Enter a comma separated list of values.
Enter NIL if there is no solution.
Answer format: 3,1,4

Answer :-

END GROUP 2

BEGIN GROUP 3

A cryptarithmetic puzzle is an arithmetic problem that is expressed using words, where words represent numbers and letters represent unique digits, i.e., different letters represent different digits. And every number (i.e., word) begins with a non-zero digit.

The task is to find out what each letter stands for, such that the arithmetic problem has a solution. Cryptarithmetic puzzles can, in general, have zero, one, or many solutions.

BABY + BEAR = HAPPY

This puzzle adds two numbers to produce a third number.
Model this puzzle as a CSP and solve it.

10. Solve the puzzle then enter the value of BEAR in the textbox, or enter NIL if no solution exists.

Answer format: 1425

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11. Solve the puzzle then enter the value of carry-digits (as a four digit number) in the textbox, or enter NIL if no solution exists.

Answer format: 0101

Answer :-

12. Solve the puzzle and enter the solution in the textbox, or enter NIL if no solution exists.

Enter the solution in the format: BABY+BEAR=HAPPY
DO NOT ENTER ANY EXTRANEOUS CHARACTER
Answer format: 1213+1425=61773

Answer :-

13. Solve the CSP with carry-digits as 1,0,0,0. Enter the solution in the textbox, or enter NIL if no solution exists.

Enter the solution in the format: BABY+BEAR=HAPPY
DO NOT ENTER ANY EXTRANEOUS CHARACTER
Answer format: 1213+1425=61773

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END GROUP 3

BEGIN GROUP 4

Consider a map colouring problem having 5 regions (A to E) and having the following pairs of regions adjacent to each other: { (A,B), (A,C), (A,E), (B,C), (B,D), (B,E), (C,D), (D,E) }.

The domains are:

D_A= D_B = D_C = [b,g,r]
D_D= D_E = [b,g]

Process the regions in the order [A,B,C,D,E] and process the values in the order [b,g,r].

The Generalized-Look-Ahead algorithm with Select-Value-Forward-Checking is solving the map colouring problem, and it has produced the partial assignment [A=b].

When we say “a variable is assigned a value” we refer to the variable assignment in Generalized-Look-Ahead procedure and not in Select-Value-Forward-Checking subprocedure.

14. What is the next variable that will be assigned a value? What value will be assigned to it?

Enter the variable and its value as a comma separated list.
Answer format: VARIABLE,VALUE

Answer :-

15. What are the values in the domain DC of region C at this point (after the variable in Question 14 was assigned a value)?