# ps9 - Massachusetts Institute of Technology 16.410...

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Problem 1 –Directed Resolution and DPLL Consider a theory Φ comprised of the following three sentences: ( R S ) P R Q ( P QR ) ¬∧∨ Part A – Conjunctive Normal Form Reduce Φ to a set of clauses. If your answer is correct, you should have four clauses. Show all steps in your reduction. Part B – Directed Resolution Derive ALL consistent assignments to P, Q, R and S using directed resolution (also known as bucket elimination). This method was covered in the lecture notes. Perform variable elimination in alphabetical order (P, Q, R and then S). Provide all consistent assignments found. Show your work. Part C – DPLL Derive ALL consistent assignments to P, Q, R and S using the DPLL algorithm. Show the full search tree, including the results of unit propagation at each step, and the result of any sub-tree pruning. Provide all consistent assignments found. Your answers to Part B and C should agree.
Problem 2 – Model-based Diagnosis In this problem you will use Single_Fault_w_Conflicts, the constraint suspension algorithm presented in lecture, to diagnose the following “Quad Or” circuit: A = 0 Y = 0 B = 0 C Z = 0 D O1 O3 I1 I2 V U S T O2 O4 The circuit is composed of four Or gates and two Inverters. Variables A, B, C, D, S, T, U, V, Y and Z are Boolean, that is their domains are {0, 1}. There are mode variables for the Or gates (denoted O1, O2, O3 and O4), and Inverters (denoted I1 and I2). The domain of each mode variable is {G, U}, where G denotes the component being good, and U denotes the component being in an unknown failure mode.

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ps9 - Massachusetts Institute of Technology 16.410...

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