$3.)$ Examine the constraint graph below, which has four variables $($X$1,$ X$2,$ X$3$ and X$4)$ and the

following three constraints:

abs$($X$1-$ X$4)<=2$

abs$($X$4-$ X$3)>=3$

X$2=$ X$1+$ X$4$

In addition, for all Xi $($e$.$g$.,$ X$1,$ X$2,$ X$3,$ X$4),$ the domains are:

Xi $=\{0,1,2,3,4,5,6,7,8,9,10\}$

a$.$ Assume that your CSP backtracking algorithm has already assigned X$1$ as $7,$ as seen

in the first row of the table below $($as of now, the domains of X$2,$ X$3$ and X$4$ still

include all possible values $(1-10)).$ Use the remaining rows to perform arcconsistency to eliminate domain values.

It does NOT matter what order you remove values but be sure to only remove values

from one variable from line to line.

X$1$ X$2$ X$3$ X$4$

$7123456789101234567891012345678910$

b$.$ What did you discover from performing arc$-$consistency in $($a$)?$ Should we pick a new

variable to expand? If so$,$ which variable? If not, should we backtrack and what does

that mean?

Dr$.$ Samuel Sambasivam HW $4$ CORE $301-$ AAI

c$.$ Now, this time assume that your CSP backtracking algorithm has already assigned X$1$

as $4($instead of $7),$ as seen in the first row of the table below $($as of now, the

domains of X$2,$ X$3$ and X$4$ still include all possible values $(1-10)).$ Use the remaining

rows to perform arc$-$consistency to eliminate domain values.

It does NOT matter what order you remove values but be sure to only remove values

from one variable from line to line.

X$1$ X$2$ X$3$ X$4$

$4123456789101234567891012345678910$

d$.$ What did you discover from performing arc$-$consistency in $($c$)?$ Should we pick a new

variable to expand? If so$,$ which variable? If not, should we backtrack and what does

that mean?