CSE330 Artificial Intelligence End-Course Assessment 2 Question | FAU

CSE330 ECA – 2

Lecturer: Kyriacos Neocleous

1. (7.5 points) Constraint Satisfaction Problem

Consider the graph with 8 nodes A₁,A₂,A₃,A₄,H,T,F₁,F₂. Each A_i is connected to A_i+1 for all i, each A_i is connected to H, H is connected to T, and T is connected to each F_i.

Find a 3-coloring of this graph by hand using the following strategy:

• Use backtracking with conflict-directed backjumping, • Follow the variable order: A₁, H, A₄, F₁, A₂, F₂, A₃, T • Use the value order (colors):

Red (R),       Green (G),       Blue (B)

2. (7.5 points) Suppose we have the formula (x₁ ⇒ x₂)∧((x₁ ⇔ x₃) ⇒ (x₁∨ x₅))∧(x₄∨¬x₂)∧((x₅∨x₂) ⇒ (x₅∧x₂))∧(x₃ ⇔ x₅)∧(x₃ ⇔¬x₄).

• Find the CNF for the above formula.
• Run the algorithm DPLL-recursive (F,ρ) on the above formula by finding the intermediate steps (F_i,ρ_i).

Is the formula satisfiable? If so, provide a solution.

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