rc consistency in constrained satisfaction problems Suppose that we have three variables X1, X2 and X3, which are defined on the same domain of {1, 2, 3}. Two binary constraints for these three variables are defined according to the following: 1. Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between R1 and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1),(1, 2),(1, 3),(3, 3)]} that switches the element order of every two-tuple of R13)? and why? 2. Suppose that, after some inference, the domain of X1 is reduced as {2, 3} and the constrains in R12 and R13 for X1 = 1 are removed accordingly. To be more specific, (1, 2) is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 still arc-con
Arc consistency in constrained satisfaction problems
Suppose that we have three variables X1, X2 and X3, which are defined on the same domain of {1, 2, 3}. Two binary constraints for these three variables are defined according to the following:
1. Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between R1 and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1),(1, 2),(1, 3),(3, 3)]} that switches the element order of every two-tuple of R13)? and why?
2. Suppose that, after some inference, the domain of X1 is reduced as {2, 3} and the constrains in R12 and R13 for X1 = 1 are removed accordingly. To be more specific, (1, 2) is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 still arc-consistent with respect X1 if the constraints between R1 and R3 are undirected? and why?
![R12 = {(X1, X2) , [(2, 1) , (2, 3) , (3, 2) , (3, 3)]}
R13 = {(X1, X3) , [(1,2) , (2, 1) , (3, 1) , (3, 3)]}
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