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Unformatted text preview: 10/27/10 1 Optimal Satisfiability and Conflictdirected A* Brian C. Williams 16.410 / 16.413 October 27 th , 2010 Brian C. Williams, copyright 2000 Assignment Remember: Problem Set #6 Propositional Logic, due Today. 16:413 Project Part 1: Satbased Activity Planner, due Wednesday, November 3 rd . Problem Set #7 Diagnosis, Conflictdirected A* and RRTs, due Wednesday, November 10 th . Reading Today: Brian C. Williams, and Robert Ragno, "Conflictdirected A* and its Role in Modelbased Embedded Systems," Special Issue on Theory and Applications of Satisfiability Testing, Journal of Discrete Applied Math , January 2003. 11/02/09 copyright Brian Williams, 200010 2 Image credit: NASA. 10/27/10 2 When you have eliminated the impossible, whatever remains, however improbable, must be the truth.  Sherlock Holmes. The Sign of the Four . Modelbased Diagnosis as Confictdirected Best First Search 1. Generate most likely Hypothesis. 2. Test Hypothesis. 3. I Inconsistent, learn reason or inconsistency (a Confict ). 4. Use conficts to leap over similarly ineasible options to next best hypothesis. Compare Most Likely Hypothesis to Observations Helium tank Fuel tank Oxidizer tank Main Engines Flow 1 = zero Pressure 1 = nominal Pressure 2 = nominal Acceleration = zero It is most likely that all components are okay. 10/27/10 3 Isolate Conflicting Information Helium tank Fuel tank Oxidizer tank Main Engines Flow 1 = zero The red component modes confict with the model and observations. Helium tank Fuel tank Oxidizer tank Main Engines Flow 1 = zero Leap to the Next Most Likely Hypothesis that Resolves the Conflict The next hypothesis must remove the confict. 10/27/10 4 New Hypothesis Exposes Additional Conflicts Pressure 1 = nominal Pressure 2 = nominal Acceleration = zero Helium tank Fuel tank Oxidizer tank Main Engines Another confict, try removing both. Final Hypothesis Resolves all Conflicts Helium tank Fuel tank Oxidizer tank Main Engines Pressure 1 = nominal Flow 1 = zero Pressure 2 = nominal Flow 2 = positive Acceleration = zero Implementation: Confictdirected A* search. 10/27/10 5 Outline Modelbased Diagnosis Optimal CSPs Informed Search Conflictdirected A* 10/27/10 10 Constraint Satisfaction Problem CSP = <X, D X ,C> variables X with domain D X . Constraint C(X): D X {True, False}. Problem: Find X in D X s.t. C(X) is True. R , G, B G R , G Differentcolor constraint V 1 V 2 V 3 10/27/10 6 10/27/10 11 Optimal CSP OCSP= <Y, g , CSP> Decision variables Y with domain D Y . Utility function g(Y): D Y . CSP over variables <X;Y>. Find leading arg max g (Y) Y D y s.t. X D X s.t. C(X,Y) is True....
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This note was uploaded on 12/26/2011 for the course SCIENCE 16.410 taught by Professor Prof.brianwilliams during the Fall '10 term at MIT.
 Fall '10
 Prof.BrianWilliams

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