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CSP Yaron Kassner Winter 2013. Reminder Arc Consistency: the domains of pairs of variables are consistent. k-consistency: the domains of every k variables.

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Presentation on theme: "CSP Yaron Kassner Winter 2013. Reminder Arc Consistency: the domains of pairs of variables are consistent. k-consistency: the domains of every k variables."— Presentation transcript:

1 CSP Yaron Kassner Winter 2013

2 Reminder Arc Consistency: the domains of pairs of variables are consistent. k-consistency: the domains of every k variables are consistent. AC3 – an algorithm that reduces the domains of variables by enforcing arc-consistency.

3 Reminder CSP problems can be solved using search. Heuristics: – assign the variable with the minimum number of remaining values – Most constraining variable – choose the variable that constrains the most variables. – choose the least-constraining-value: the value that is inconsistent with as few other values as possible. Forward checking – after assignment, reduce domain of neighboring variables. MAC – maintain arc-consistency: do a back-tracking search, and fix arc consistency after every assignment.

4 AC-3 complexity

5 Example: Cryptarithmetic Problem TWO + TWO _____ FOUR O R C1 W U C2 T F C301 C3 C2 C1

6 TWO + TWO _____ 1OUR O R C1 W U C2 T F C31 Characters are distinct 1 C2 C1 Example: Cryptarithmetic Problem

7 TWO + TWO _____ 1OUR O R C1 W U C2 T F C31 1 C2 C1 Example: Cryptarithmetic Problem

8 TWO + TWO _____ 1OUR O R C1 W U C2 T F C31 1 C2 C1 Example: Cryptarithmetic Problem

9 TWO + TWO _____ 1OUR O R C1 W U C2 T F C31 1 C2 C1 Example: Cryptarithmetic Problem

10 TWO + TWO _____ 1OUR O R C1 W U C2 T F C31 1 C2 C1 Example: Cryptarithmetic Problem

11 TWO + TWO _____ 1OUR O R C1 W U C2 T F C C1 Example: Cryptarithmetic Problem

12 TWO + TWO _____ 1OUR O R C1 W U C2 T F C C1 Example: Cryptarithmetic Problem

13 TWO + TWO _____ 1OUR O R C1 W U C2 T F C C1 Example: Cryptarithmetic Problem

14 TWO + TWO _____ 1OUR O R C1 W U C2 T F C C1 Example: Cryptarithmetic Problem

15 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

16 TW3 + TW3 _____ 13UR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

17 TW3 + TW3 _____ 13U6 O R C1 W U C2 T F C Example: Cryptarithmetic Problem

18 6W3 + 6W3 _____ 13U6 O R C1 W U C2 T F C גלגול אחורה Example: Cryptarithmetic Problem

19 TWO + TWO _____ 1OUR O R C1 W U C2 T F C C1 Example: Cryptarithmetic Problem

20 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

21 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

22 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

23 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

24 TWO + TWO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

25 8WO + 8WO _____ 1OUR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

26 8W7 + 8W7 _____ 17UR O R C1 W U C2 T F C Example: Cryptarithmetic Problem

27 8W7 + 8W7 _____ 17U4 O R C1 W U C2 T F C Distinct character values Example: Cryptarithmetic Problem

28 _____ 17U4 O R C1 W U C2 T F C Example: Cryptarithmetic Problem

29 _____ 1734 O R C1 W U C2 T F C Example: Cryptarithmetic Problem

30 Example: Zebra puzzle 4OY 4OY Some kind of MAC.


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