ps5 - Massachusetts Institute of Technology 16.410-13...

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Massachusetts Institute of Technology 16.410-13 Principles of Autonomy and Decision Making Assignment #5, tutorial. Due: LEC #10 Problem PS.5.1.1: CSP search We will now consider a very simplified situation in which there are only four variables: A, B, C and D and each of them have only two legal values, which we will write as: A1, A2 (for variable A), B1, B2 (for variable B), C1, C2 (for variable C) and D1, D2 (for variable D). The only legal assignments for each pair of variables are: A-B : A1-B1, A2-B1 A-C : A1-C1, A2-C2 B-D : B1-D1 C-D : C2-D1 B-C : No constraint. A-D : No constraint. No other combination of variable values is legal. Let's say that that ``an assignment is generated'' every time a variable in the problem gets a new (tentative) assignment. We assume that the variables are examined in alphabetical order and the values in numerical order. Below, we ask you to solve this problem using pure backtracking and also by using backtracking with forward checking. Stop when a valid solution is found. The search tree for this problem is given below. Each node (except the root) is labeled with the value involved in the assignment, the variable involved is obvious given the value. Your answers will a space-separated sequence of these values involved in the assignments as they are generated during the appropriate search. For example, A1 B1 etc. ----------------()--------------- | | -------A1------- -------A2------ | | | | ---B1--- ---B2--- ---B1--- ---B2--- | | | | | | | | -C1- -C2- -C1- -C2- -C1- -C2- -C1- -C2- | | | | | | | | | | | | | | | | D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 1. Pure backtracking: How many total assignments are made before finding an answer? 2. Pure backtracking: Show the assignments in order
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3. Backtracking with forward checking: How many assignments are made before finding an answer? 4. Backtracking with forward checking: Show the assignments in order Problem PS.5.1.2: Crossword You are given the following simple crossword puzzle: You are also give a list of candidate words with the right length for each numbered row and column, all that remains is to select the correct word that matches the constraints of the other columns and rows: 1 across h o s e s l a s e r s h e e t s n a i l s t e e r 2 down a r o n e a r n h i k e k e e t s a m e 3 down eat let run ten yes 4 across aro n ear n hi k e kee t same 5 across be it no us A crossword puzzle imposes the constraint that words that cross must agree on the letter at the intersection where they cross. For example, one constraint is that the third letter of 1A (1 across) must agree with the first letter of 2D (2 down). We will label this constraint C12, taking the 1 from the across letter (1A) and the 2 from the down letter (2D). We have a total of five constraints in this puzzle: C12, C13, C42, C43, and C52. 1. We will start by applying pure constraint propagation. In other words there is no search at all, just constraint propagation. For each of the words listed below, indicate whether it is Ok or some constraint that would eliminate it (there may be more than one, but just pick one). In this question, you do not need to simulate the propagation process in detail. Just figure out what words are left for each variable after propagation and then look at the eliminated words and see what constraints are violated.
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This note was uploaded on 11/07/2011 for the course AERO 16.410 taught by Professor Brianwilliams during the Fall '05 term at MIT.

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ps5 - Massachusetts Institute of Technology 16.410-13...

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