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Satisfiability Generate-and-test / NP / NP-complete SAT, weighted MAX-SAT, CNF-SAT, DNF-SAT, 3-CNF-SAT, Tseitin, TAUT, QSAT Some applications: LSAT , register allocation

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Given a suitable representation for a Boolean function f(X) ... Implication. x y = x y = ( y) ( x) = y x (contra positive) ...

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The ambassador instructs you to invite Peru or exclude Qatar. The vice-ambassador wants you to invite Qatar or Romania or both. ...

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... the exponential memory requirements of DP. Exponential time is still a ... A variable is forced to be assigned to be True or False based on previous assignments ...

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Title: Chapter 34: Satisfiability Author: A. Student Last modified by: Jesus De Loera Created Date: 1/27/2003 9:18:35 AM Document presentation format

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The Computational Complexity of Satisfiability Lance Fortnow NEC Laboratories America

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Find a sequence of operators that transform an initial state to a goal state ... satz (Chu Min Li) - variable selection by forward checking: max unit props ...

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Generalizations: regular trees, context-free languages, infinite words, probabilistic automata. ... Other Logics, Probabilistic Automata ...

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dynamically growing and shrinking number of processes ... a model is built using PROMELA. property is specified. SPIN works as a verifier ...

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University Of Antwerp. 3. XPath Expressions: (subset XPath 2.0) ... University Of Antwerp. 4. Tree Description Graphs. Studied in Computational Linguistics ...

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A disjunctive formula is a collection of one or more (positive and negative) ... eliminates in one shot all that can be eliminated and returns a smaller formula. ...

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A multi-valued clause is a logical disjunction of one or more MV literals. A formula in multi-valued conjunctive normal form (MV-CNF) is the logical ...

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V (i): clauses that i appears un-negated. V- (i): clauses that i appears negated ... i appears un-negated. 42. BP in SAT Problem. Probability that xj = 1. 43 ...

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A Progressive Approach for Satisfiability Modulo Theories Hossein M. Sheini Karem A. Sakallah Electrical Engineering and Computer Science University of Michigan, Ann ...

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Boolean Satisfiability in Electronic Design Automation Jo o Marques Silva Informatics Department Technical University of Lisbon IST/INESC, CEL Karem A. Sakallah

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A Compressed Breadth-First Search for Satisfiability DoRon B. Motter and Igor L. Markov University of Michigan, Ann Arbor

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DPLL-based Checkers for Satisfiability Modulo Theories Cesare Tinelli Department of Computer Science The University of Iowa Joint work with Jed Hagen (Iowa) Robert ...

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Provably hard problems below the satisfiability threshold

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Literal - a variable (could be negated) Clause - logical OR of one or more literals ... Part 1: 'Push' the negations through the Boolean expression so that variables ...

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Input: Boolean formula F in CNF. F = (x1 OR x2) AND (x1 OR x3 OR x4) AND ... planning: all trucks at a base station, all nails in assembly ...

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Propositional logic with equations of form vi = vj. Bryant, German & Velev, CAV '99 ... Create special purpose search engine. Davis-Putnam search ...

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Applying Case Based Reasoning to Boolean Satisfiability

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Prof. Necula CS 294-8 Lecture 11. 1. Theorem Proving for FOL ... No disjunction, implication or quantification ! Is that bad ? Consider the function: ...

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Much design and implementation work has gone into creating SAT solvers, like chaff. ... Ships may not intersect or share adjacent grid cells, even diagonally. ...

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... (Boolean) logic only involves propositional symbols and operators ... (non-logical symbols) and their meanings ... can take any meaning ...

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in an infinite model of T. CMU, Oct 4. Talk Plan ... New version of the DPLL(T) calculus, to model more accurately modern SAT engines ...

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Given a formula, f : C1. C2. C3. a=b=c=1 (a,b,c) (C1,C2,C3) Comprised ... SAT: Seek an assignment of to the variables, V, which sets the Boolean formula to 1' ...

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Given: a subject graph representing the circuit (usually a netlist of 2-input gates) ... of a root node and its predecessors such that any node within the cone ...

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1. Modeling and Solving Planning Problems as ... ORL. NYC. 38. Pruning the Planning Graph. Category I Rules. Facts. Facts. Actions. Facts. Facts ... ORL. NYC ...

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SAT is the quintessential NP-complete problem. Theoretically well-studied. Practical algorithms for large problem instances started emerging in the last five years ...

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Jo o Marques-Silva. Informatics Department. Technical University of Lisbon. IST/INESC, CEL ... Practical algorithms for large problem instances started emerging ...

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We cannot bet on any breakthrough without fundamentally change the way the algorithm works. i.e. Don't bet on another 3 orders of magnitude speed up in the next 10 ...

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Comparing Extremal and Hysteretic Optimization on the Satisfiability Problem ... Extremal Optimization (1) Start with random configuration. Order the variables ...

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Given a suitable representation for a Boolean function : ... valid or tautology if for all T. unsatisfiable if for any T. VALID. SATISFIABLE. UNSATISFIABLE ...

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When the animated 'Creature Buddies' go on tour, they are played by puppets. Creatures: Dragon, Gorilla, Kangaroo, Tiger. Names: Audrey, Hamish, Melville, Rex ...

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Domain knowledge ' constraints on search and solution spaces ... Easy to encode domain-specific knowledge in the planning as satisfiablity frame ...

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Satisfiability modulo the Theory of Bit Vectors

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Find a (partially) ordered set of actions that transforms a ... Related work: Walsh '03; Gent, Nightingale, and Stergiou '05; Pan & Vardi 04; Giunchiglia et al. ...

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Small crossword grid medium-sized dictionary may turn into a big formula ... across solver types. systematic (last lecture) stochastic (this lecture) ...

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Satisfiability Modulo Theories Sinan Hanay Boolean Satisfiability (SAT) Satisfiability Modulo Theories (SMT) SAT vs SMT SMT extends SAT solving by adding extensions ...

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The problem of finding an assignment to a set of variables that satisfies a ... Hirsch (2000) Sch ning (1999) Iwama, Tamaki (2003) Iwama, Tamaki (2003) Who. O(1.2388m) ...

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... a Characteristic Function for circuits (also creates ... Derive characteristic function H for circuit g. Replace all instances of g in H with f ...

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Bsolo (Manquinho and Marques-Silva, 2002) is based on old SAT solver GRASP. ... Presented an efficient solver MinCostChaff that applies advanced techniques in ...

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Complexity Analysis of a Massively Parallel Boolean Satisfiability ... cannot be a part of any satisfying assignment we can add a clause forbidding it. ...

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Efficient Methods for Solving Finite Satisfiability Problems in UML Class ... Consider the pervious example: 10. Infinity Problem (2) 11. Relevance of Reasoning ...

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Both the AI and CADE/CAV communities have long been concerned with reasoning ... 'Classic' work in AI has concentrated on STRIPS style planning ('state space' ...

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Solution of a Satisfiability Problem on a Gen-based DNA Computer ... Johnson, Paul W.K. Rothemund, Darryl Hwang, Nickolas Chelyapov and Leonard M. Adleman ...

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GRASP: A Search Algorithm for Propositional Satisfiability Conflict Clause Significantly prune the search speace Learned clause is useful forever Useful in generating ...

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Equality between two strings (trees) : (e2, e) Tolerant ... Non determinism and Probabilistic. Can we combine both non determinism and probabilistic behaviors? ...

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Logical formula in conjunctive normal form (AND of OR-clauses): (x1 or not(x2) ... 13. Metropolis Algorithm. Simulated Annealing: Gradually decrease T ...

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Title: Layout-Driven Synthesis for Submicron Technology: Mapping Expansions to Regular Lattices Author: Last modified by: Marek Created Date

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A Compressed Breadth-First Search for Satisfiability. DoRon B. Motter and Igor L. Markov ... The DP procedure: Simon and Chatalic, IJCAI 2000. DLL: Aloul, ...

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Fred Glover. Bahram Alidaee. Keith Womer. Haitao Li. Introduction: ... w Three possible clause types. w Each with linear constraint ...

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MBSat Satisfiability Program and Heuristics Brief Overview VLSI Testing 304-649B Marc Boul April 2001 McGill University Electrical and Computer Engineering

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Using Boolean Satisfiability for Path Sensitive Analysis ... Backend for many tools in verification, AI, etc. Much recent work: Chaff / Grasp / SATO / GSAT ...

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MiniSat, BerkMin, Siege, zChaff, Limmat, GRASP, SATO. Conversion to CNF by adding new variables ... Siege. BerkMin. MiniSat. SatMate. Problem. 25. Conclusion ...

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