Artificial Intelligence - Approaches to Artificial Intelligence

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Consider a SAT problem where formula F is given by:
F = (a v ¬b) ∧ (¬a v b v c) ∧ (¬c v d) ∧ d ∧ (¬a v b v d) ∧ (¬a v ¬d)
The heuristic function h(F) returns the number of satisfied clauses in the formula F. Observe that one has to maximize the heuristic value. A candidate assignment, or state, is of the form (abcd). If the state is 0000, then the assignment is a a=0, b=0, c=0 and d=0. Let the MoveGen function be such that it changes 1 bit in a candidate. For example, from the state 0000 with one-bit change we get 0001, 0010, 0100 and 1000 as the neighbors. Now let the initial state be 1010.

26. What are the values returned by h(F) for the assignments 0000, 0110 and 1011?

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27. Given the start state in the above problem, which move from the set {R, L, U} could be chosen by the Hill Climbing algorithm using the heuristic function h2
1. R
2. U
3. L

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Consider a SAT problem where formula F is given by:
F = (a v ¬b) ∧ (¬a v b v c) ∧ (¬c v d) ∧ d ∧ (¬a v b v d) ∧ (¬a v ¬d)
The heuristic function h(F) returns the number of satisfied clauses in the formula F. Observe that one has to maximize the heuristic value. A candidate assignment, or state, is of the form (abcd). If the state is 0000, then the assignment is a a=0, b=0, c=0 and d=0. Let the MoveGen function be such that it changes 1 bit in a candidate. For example, from the state 0000 with one-bit change we get 0001, 0010, 0100 and 1000 as the neighbors. Now let the initial state be 1010.

28. Simulate the Hill Climbing algorithm for the above SAT problem. If the algorithm randomly chooses a move in case there is a tie, what is the probability of the algorithm solving the above SAT problem?

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Consider a SAT problem where formula F is given by:
F = (a v ¬b) ∧ (¬a v b v c) ∧ (¬c v d) ∧ d ∧ (¬a v b v d) ∧ (¬a v ¬d)
The heuristic function h(F) returns the number of satisfied clauses in the formula F. Observe that one has to maximize the heuristic value. A candidate assignment, or state, is of the form (abcd). If the state is 0000, then the assignment is a a=0, b=0, c=0 and d=0. Let the MoveGen function be such that it changes 1 bit in a candidate. For example, from the state 0000 with one-bit change we get 0001, 0010, 0100 and 1000 as the neighbors. Now let the initial state be 1010.

29. Simulate the Beam Search algorithm, with beam width 2, for the above SAT problem. Assume that if there are more than two bet candidates, the algorithm randomly picks any two from them. What is the probability of the algorithm solving the above SAT problem?

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30. Assume that if there are more than two best candidates, Beam Search with beam width 2 randomly picks any two from them. Which distinct pairs of 2 candidates at level 2 (after two expansion) could be best two candidates?
1. 0000, 1001
2. 0011, 1111
3. 0000, 0011
4. 0110, 1110

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