grasp - GRASP-an efficient SAT solver Pankaj Chauhan What...

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1 GRASP-an efficient SAT solver Pankaj Chauhan 9/20/01 15-398: GRASP and Chaff 2 What is SAT? n Given a propositional formula in CNF, find an assignment to boolean variables that makes the formula true! n E.g. w 1 = (x 2 x 3 ) w 2 = ( x 1 x 4 ) w 3 = ( x 2 x 4 ) A = {x 1 =0, x 2 =1, x 3 =0, x 4 =1} SATisfying assignment!
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2 9/20/01 15-398: GRASP and Chaff 3 What is SAT? n Solution 1: Search through all assignments! n n variables 2 n possible assignments, explosion! n SAT is a classic NP-Complete problem, solve SAT and P=NP! 9/20/01 15-398: GRASP and Chaff 4 Why SAT? n Fundamental problem from theoretical point of view n Numerous applications n CAD, VLSI n Optimization n Model Checking and other type of formal verification n AI, planning, automated deduction
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3 9/20/01 15-398: GRASP and Chaff 5 Outline n Terminology n Basic Backtracking Search n GRASP n Pointers to future work Please interrupt me if anything is not clear! 9/20/01 15-398: GRASP and Chaff 6 Terminology n CNF formula j n x 1 ,…, x n : n variables n w 1 ,…, w m : m clauses n Assignment A n Set of (x,v(x)) pairs n |A| < n partial assignment {(x 1 ,0), (x 2 ,1), (x 4 ,1)} n |A| = n complete assignment {(x 1 ,0), (x 2 ,1), (x 3 ,0), (x 4 ,1)} n j | A = 0 unsatisfying assignment {(x 1 ,1), (x 4 ,1)} n j | A = 1 satisfying assignment {(x 1 ,0), (x 2 ,1), (x 4 ,1)} w 1 = (x 2 x 3 ) w 2 = ( x 1 x 4 ) w 3 x 2 x 4 ) A = {x 1 =0, x 2 =1, x 3 =0, x 4 =1}
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4 9/20/01 15-398: GRASP and Chaff 7 Terminology n Assignment A (contd.) n j | A = X unresolved {(x 1 ,0), (x 2 ,0), (x 4 ,1)} n An assignment partitions the clause database into three classes n Satisfied, unsatisfied, unresolved n Free literals : unassigned literals of a clause n Unit clause : #free literals = 1 9/20/01 15-398: GRASP and Chaff 8 Basic Backtracking Search n Organize the search in the form of a decision tree n Each node is an assignment, called decision assignment n Depth of the node in the decision tree decision level d (x) n x=v@d x is assigned to v at decision level d
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5 9/20/01
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This note was uploaded on 02/29/2012 for the course CS 15-453 taught by Professor Edmundm.clarke during the Spring '09 term at Carnegie Mellon.

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grasp - GRASP-an efficient SAT solver Pankaj Chauhan What...

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