Concordia University Constraint Satisfaction in the Artificial Intelligence Problems

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nehavn23887

Computer Science

Concordia University St Paul

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Hi, I need solutions for the questions in the doc.

Clarification:

4.4: Assume that the domain of each variable has already been constrained by unary constraints before the assignment of 5 to variable T, and pay attention to the order in which arc-consistency should be applied to each variable.

4.1: typo with the second carry variable in constraint (e), should be: c1 + E + E + A = 10 * c2 + E

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4. Constraint Satisfaction Problems (8 + 2 points) In this puzzle, each of the following letters is a variable that can be assigned to a numerical digit from 0 to 9. c​ 4 c​ ​ 3 ​ c​ 2​ c​ 1 T + C A L E T H E M E A T K E S Carry variables are denoted as c​1​, c​2​, c​3​, and c​4​. 4.1 All the constraints for this problem are defined in the following table. For each constraint, enter ​ONE​ of “unary”, “binary”, or “n-ary” to describe the type of constraint. ​(1 Point) Constraint a) Alldiff(A, C, E, H, K, L, M, S, T), meaning each variable must be assigned a unique digit b) L, T, E, and C must not be assigned the digit 0 c) Carry variables must only be assigned 0, 1, or 2 d) T + M + T = 10 * c​1​ + S e) c​1​ + E + E + A = 10 * c​1​ + E f) c​2​ + L + H + E = 10 * c​3​ + K g) c​3​ + T = 10 * c​4​ + A h) c​4​ = C Page 10 out of 61 Type 4.2 Based on the constraint hypergraph for this problem, fill in the table below representing the adjacency matrix. The elements of the matrix should be the number of arcs (hypernodes/hyperedges) between any two variables (each unary constraint contributes one self-referential arc for that variable). ​(3 Points) c​1 c​2 c​3 c​4 A C E H c​1 c​2 c​3 c​4 A C E H K L M S T Page 11 out of 61 K L M S T 4.3 What domain of T would allow the graph to remain arc-consistent? (Enter the domain as a comma-separated list of digits, e.g. “0, 4, 6, 7, 9”). ​(1 point) ____________________________________________________________________ 4.4 Suppose you assign 5 to variable T, and apply constraint propagation (arc-consistency) to each variable in alphabetical order (with carry variables last). What is the domain of A? ​(3 points) ____________________________________________________________________ Is the graph arc-consistent? If not, specify which variable(s) have an empty domain (if any), and/or which constraint(s) are arc-inconsistent. Otherwise, enter “none”. Variable(s), e.g., “c1, A, C, S” Constraint(s), e.g., “b, g” 4.5 Solve this CSP. There are multiple unique solutions (you only need to find one of them). Show your work in the empty right hand column. ​(2 points - Bonus) Variable Result c​1 c​2 c​3 c​4 A C E H K L M S T Page 12 out of 61
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Anonymous
Great study resource, helped me a lot.

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