ps9 - Massachusetts Institute of Technology 16.410...

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Massachusetts Institute of Technology 16.410 Principles of Automated Reasoning and Decision Making Problem Set #9 written part Due: Session 22 16.410 Programming part Due: by 5pm Session 23 Logic Inference, Diagnosis and State Estimation Objectives In this problem set we continue the development of your understanding of logical reasoning and its application, and then extend the development to probabilistic systems. In particular, first, we exercise your understanding of inference using directed resolution. Next we exercise your understanding of consistency based diagnosis and conflict-directed search on a simple model-based diagnosis problem. Finally, we exercise your understanding of probabilistic state estimation on Hidden Markov models, using the Viterbi and Baum-Welch Algorithms. Note that both 16.410 and 16.413 students will exercise their understanding of HMMs through a problem worked out by hand. In addition, ONLY 16.410 students will exercise their understanding through a JAVA coding exercise. Note, however, that a 16.413 student CAN choose to perform this coding exercise, in order to make up for a missed programming exercise on a previous assignment. Readings Please read the lecture notes for coverage of propositional inference and model-based diagnosis. Please also read the lecture notes on HMM algorithms. You should also have already read AIMA Chapter 7, for problem set #9. For a basic review of probabilities, read AIMA Chapter 13. Finally, for state estimation and Hidden Markov Models, read the lecture notes and AIMA Chapter 15, all sections except 15.5.
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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.
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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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