# Week5 - CSE 3402 Intro to Artificial Intelligence CSPs...

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1 1 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance CSE 3402: Intro to Artificial Intelligence CSPs & Backtracking Search Readings: Chapter 6. 2 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems The search algorithms we discussed so far had no knowledge of the states representation (black box). So, we could not take advantage of domain-specific information. CSP are a special class of search problems with a uniform and simple state representation. This allows to design more efficient algorithms.

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2 3 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems Many problems can be represented as a search for a vector of feature values. k-features: variables. Each feature has a value. Domain of values for the variables. e.g., height = {short, average, tall}, weight = {light, average, heavy}. In these problems the problem is to search for a set of values for the features (variables) so that the values satisfy some conditions (constraints). 4 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems Sudoku: 81 variables, the value in each cell. Values: a fixed value for those cells that are already filled in, the values {1-9} for those cells that are empty. Solution: a value for each cell satisfying the constraints: no cell in the same column can have the same value. no cell in the same row can have the same value. no cell in the same sub-square can have the same value.
3 5 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems Scheduling Want to schedule a time and a space for each final exam so that No student is scheduled to take more than one final at the same time. The space allocated has to be available at the time set. The space has to be large enough to accommodate all of the students taking the exam. 6 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems Variables: T1, …, Tm: Ti is a variable representing the scheduled time for the i-th final. Assume domains are fixed to {MonAm, MonPm, …, FriAm, FriPm}. S1, …, Sm: Si is the space variable for the i-th final. Domain of Si are all rooms big enough to hold the i-th final.

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4 7 CSE 3402 Winter 2012 Fahiem Bacchus & Yves Lesperance Constraint Satisfaction Problems Want to find an assignment of values to each variable (times, rooms for each final), subject to the constraints: For all pairs of finals i, j such that there is a student taking both: Ti Tj For all pairs of finals i, j Ti Tj or Si Sj either i and j are not scheduled at the same time, or if they are they are not in the same space. 8
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Week5 - CSE 3402 Intro to Artificial Intelligence CSPs...

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