Approaches to AI 29

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.

0. 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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