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72 Pages

### lec08

Course: ECE 156, Fall 2009
School: UCSB
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Word Count: 3074

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Satisfiability Boolean in Electronic Design Automation Joo Marques-Silva Informatics Department Technical University of Lisbon IST/INESC, CEL Karem A. Sakallah EECS Department University of Michigan Context SAT is the quintessential NP-complete problem Theoretically well-studied Practical algorithms for large problem instances started emerging in the last five years Has many applications in EDA and other...

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Satisfiability Boolean in Electronic Design Automation Joo Marques-Silva Informatics Department Technical University of Lisbon IST/INESC, CEL Karem A. Sakallah EECS Department University of Michigan Context SAT is the quintessential NP-complete problem Theoretically well-studied Practical algorithms for large problem instances started emerging in the last five years Has many applications in EDA and other fields Can potentially have similar impact on EDA as BDDs EDA professionals should have good working knowledge of SAT formulations and algorithms Outline Boolean Satisfiability (SAT) Basic Algorithms Representative EDA Applications Taxonomy of Modern SAT Algorithms Advanced Backtrack Search Techniques Experimental Evidence Conclusions Boolean Satisfiability Given a suitable representation for a Boolean function f(X): Find an assignment X* such that f(X*) = 1 Or prove that such an assignment does not exist (i.e. f(X) = 0 for all possible assignments) In the "classical" SAT problem, f(X) is represented in product-of-sums (POS) or conjunctive normal form (CNF) Many decision (yes/no) problems can be formulated either directly or indirectly in terms of Boolean Satisfiability Conjunctive Normal Form (CNF) = ( a + c ) ( b + c ) (a + b + c ) Clause Positive Literal Negative Literal Basics Implication x y = x + y = (y) + (x) = y x (contra positive) Assignments: {a = 0, b = 1} = a b Partial (some variables still unassigned) Complete (all variables assigned) Conflicting (imply ) = (a + c)(b + c)(a + b + c) (a + c) (a + c) Consensus General technique for deriving new clauses Example: 1 = (a + b + c), 2 = (a + b + d) Consensus: con( 1, 2, a) = (b + c + d) Complete procedure for satisfiability [Davis, JACM'60] Impractical for real-world problem instances Application of restricted forms has been successful! E.g., always apply restricted consensus con((a + ), (a + ), a) = () is a disjunction of literals Literal & Clause Classification violated satisfied unresolved satisfied = (a + b)(a + b + c )(a + c + d )(a + b + c ) a as...
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