cs188_sp09_mt1_sol 5

# cs188_sp09_mt1_sol 5 - E 1,E n-1 correspond to the...

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NAME: 5 Now consider a chain structured graph over variables X 1 ,...,X n . Edges E 1 ,...,E n - 1 connect adjacent variables, but their directions are again unknown. X 1 X 2 X n E 1 E 2 E n-1 g) (4 pt) Using only binary constraints and two-valued variables, formulate a CSP that is satisﬁed by only and all networks that can represent a distribution where X 1 6⊥⊥ X n . Describe what your variables mean in terms of direction of the arrows in the network. Variables: Variables E 1 ,...,E n - 1 correspond to the directions of these edges and take values { left,right } . Constraints: ( E i ,E i +1 ) 6 = ( right,left ), for i ∈ { 0 ,...,n - 2 } . h) (6 pt) Using only unary, binary and ternary (3 variable) constraints and two-valued variables, formulate a CSP that is satisﬁed by only and all networks that enforce X 1 ⊥⊥ X n . Describe what your variables mean in terms of direction of the arrows in the network. Hint: You will have to introduce additional variables. Variables: Variables
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Unformatted text preview: E 1 ,...,E n-1 correspond to the directions of these edges and take values { left,right } . I 1 ,...,I n-2 can take values { T,F } . O 1 ,...,O n-2 can take values { T,F } . Constraints: Intuitively, we want I i to be T if X i → X i +1 ← X i +2 , i.e. the triple X i ,X i +1 ,X i +2 is inactive. Also, we want O i to be T if either I i or O i-1 is T, i.e. if the current triple is inactive or if any of the prior triples was inactive. Finally, we want O n-2 to be T which would imply that there is some inactive triple. ( I i ,E i ,E i +1 ) ∈ { ( T,right,left ) , ( F,right,right ) , ( F,left,right ) , ( F,left,left ) } for i ∈ { 1 ,...,n-2 } . ( I 1 ,O 1 ) ∈ { ( T,T ) , ( F,F ) } ( O i-1 ,I i ,O i ) ∈ { ( F,F,F ) , ( F,T,T ) , ( T,F,T ) , ( T,T,T ) } for i ∈ { 2 ,...,n-2 } O n-2 = true...
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## This note was uploaded on 08/30/2009 for the course CS 188 taught by Professor Staff during the Spring '08 term at Berkeley.

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