1. Alexander Felfernig and Müslüm Atas Institut für Softwaretechnologie
Klassische Themen der Computerwissenschaft - Constraint Satisfaction: Exercises -
Alexander Felfernig and Müslüm Atas
Institut für Softwaretechnologie
Inffeldgasse 16b/2
A-8010 Graz
Austria

2. Exercises Part 1

3. Exercise 1 (1 Point)
Given the following CSP. V={wr,ip,rr} dom(wr)={low,medium,high}; dom(ip)={short-t, medium-t, long-t}; dom(rr)={‘1-3%’,’>3-6%’, ’>6-9%’,’>9%’} C={c1, c2, c3, c4, c5} c1: ┐(wr=medium)  ip<>short-t c2: wr=high  ip=long-t c3: ip=long-t  rr=‘>3-6%’  rr=‘>6-9%’ c4: rr=‘>9%’  wr<>medium  wr<>low c5: rr=‘>6-9%’  wr<>low  wr<>medium Show that the given CSP has a solution.

4. Exercise 2 (3 Points)
Given the following CSP. V={v1,v2,v3} dom(v1) = dom(v2) = dom(v3) = {1..4} C={c1,c2,c3} c1:v1=v2 c2:v2>v3 c3:v3>1 Show the determination of a solution for the given CSP on the basis of backtracking and forward checking.

5. Exercise 3 (6 Points)
Download the Java Constaint Solving Library CHOCO (ver. 4.0) (documentation is included):
A) Define your own CSP on the basis of CHOCO with:
20 variables
100 constraints (50 binary, 50 n-ary)
B) Calculate and show all solutions.

6. CHOCO
Version: Use for the exercises General Information, JavaDoc, Tutorials and more: How to use locally (Maven):

7. Summary of Exercises Part 1
Explain your solutions for all exercises in a .pdf. Send the .pdf and the CHOCO sources (as a .java-File) to: The relevant deadline for submitting your solutions is contained in the lecture slides.

8. Exercises Part 2

9. Exercise 4 (2 Points) Given the following CSP. V={v1,v2,v3}
dom(v1) = dom(v2) = dom(v3) = {1..4}
C={c1,c2,c3}
c1:v1>v2
c2:v2>v1
c3:v3<>v1
Determine all minimal conflict sets in C on the basis of the Simple Conflict Detection Algorithm.

10. Exercise 5 (4 Points)
On the basis of your CSP defined in Exercise 3, include the following aspects/functionalities in your CHOCO based implementation.
A) Convert the CSP (defined in CHOCO) from Exercise 3: the “new” CSP (also defined in CHOCO) must be inconsistent (no solution exists) and contain at least 12 minimal conflict sets and at least 10 minimal diagnoses.
B) Determine one minimal conflict set in the CSP with your own implementation of SimpleConflictDetection.

11. Exercise 6 (2 Points)
Explain how QuickXPlain exploits the idea of “divide-and-conquer” on the basis of a simple example.

12. Exercise 7 (2 Points)
Explain the concept of “arc consistency” on the basis of a simple example.

13. Summary of Exercises Part 2
Explain your solutions for all exercises in a .pdf. Send the .pdf and the CHOCO sources (as a .java-File) to: The relevant deadline for submitting your solutions is contained in the lecture slides.

14. Thank You!