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info372-hw5-sol

# info372-hw5-sol - Info 372 Homework 5 Solutions 1 Consider...

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Info 372 Homework 5 - Solutions 1. Consider the crossword puzzle given below: Suppose we have the following words in our dictionary: laser, sails, hoses, sheet, steer, heel, hike, keel, knot, line, aft, ale, eel, lee, tie . (a) Specify the problem as a constraint satisfaction problem. (20 points) We have eight variables corresponding to the words: 1A, 2D, 3D, 4A, 5D, 6D, 7A, 8A. The domain for 1A, 2D, 3D and 8A is { laser , sails , hoses , sheet , steer } . The domain for 4A and 5D is { heel , keel , knot , line } . The domain for 7A and 6D is { a f t , ale , eel , lee , tie } . Constraints: 1A[3] = 2D[1] 1A[5] = 3D[1] 2D[3] = 4A[2] 2D[4] = 7A[1] 2D[5] = 8A[3] 3D[3] = 4A[4] 3D[4] = 7A[3] 3D[5] = 8A[5] 4A[3] = 5D[1] 5D[2] = 7A[2] 5D[3] = 8A[4] 6D[2] = 8A[1] (b) Give an example of pruning through arc consistency. (10 points) Consider the domains for 6D and 8A. Arc consistency means that for each value in 6D’s domain there exists a value in the domain of 8A, such that the two values are consistent (i.e., they don’t violate any constraints). An example is: consider the word “tie” in the domain of 6D; since no 5 letter word starts with “i” (i.e., no value in the

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