need help in AI/ machine learning problem, topic- CSP

3- CSP Suppose we have a CSP with 4 variables X1, X2, X3,X4 E 0,1) and 3 factors ti, i E 1,2,3) t1, t2, t3 are binary XOR functions between X1, X2, X3 (t (X)x;Dxi-i,i E (1,2)). t3 is a factor among all X1, X2,X3, X4: t3 (X)xiVx2Vx3Vx4 a) Draw the factor graph for this problem b) How many consistent assignments are there for this CSP? c) If we use backtracking search to solve the CSP without using any heuristics (MCV, LCV, AC-3) or lookahead, how many times will backtrack() be called to get all consistent assignments if we use the fixed ordering X1,X3,X2,X4? (You should use the Backtrack algorithm from the slides. The initial arguments are x, w=1, and the original Domain.) d) If we use ordering X1,X3,X2,X4 and AC-3, how many times will Backtrack be called to get all consistent assignments? Explain why. How can we reduce this CSP to one with only unary and/or binary constraints? Explain what auxiliary variables we need to introduce, what their domains are, what unary/binary factors you'll add, and why your scheme works. Add a graph if you think that'll better explain your scheme e) 3- CSP Suppose we have a CSP with 4 variables X1, X2, X3,X4 E 0,1) and 3 factors ti, i E 1,2,3) t1, t2, t3 are binary XOR functions between X1, X2, X3 (t (X)x;Dxi-i,i E (1,2)). t3 is a factor among all X1, X2,X3, X4: t3 (X)xiVx2Vx3Vx4 a) Draw the factor graph for this problem b) How many consistent assignments are there for this CSP? c) If we use backtracking search to solve the CSP without using any heuristics (MCV, LCV, AC-3) or lookahead, how many times will backtrack() be called to get all consistent assignments if we use the fixed ordering X1,X3,X2,X4? (You should use the Backtrack algorithm from the slides. The initial arguments are x, w=1, and the original Domain.) d) If we use ordering X1,X3,X2,X4 and AC-3, how many times will Backtrack be called to get all consistent assignments? Explain why. How can we reduce this CSP to one with only unary and/or binary constraints? Explain what auxiliary variables we need to introduce, what their domains are, what unary/binary factors you'll add, and why your scheme works. Add a graph if you think that'll better explain your scheme e)