PPT-SAT tutorial 1 Boolean Satisfiability in Electronic Design Automation

Karem A Sakallah EECS Department University of Michigan João Marques Silva Informatics Department Technical University of Lisbon ISTINESC CEL SAT tutorial 2 Context SAT is the quintessential NPcomplete problem. Goal: . Show . how . propositional equivalences . are established . & introduce . the most . important such . equivalences.. Copyright © Peter . Cappello. 2. Equivalence. Name. p .  T . ≡ p; p . Lecture 4 – Part 2. M. Pawan Kumar. pawan.kumar@ecp.fr. Finite set . Σ. called alphabet of size ≥ 2. {0,1}. {. a,b,c,d,e. ,…,. x,y,z. }. Set . Σ. * of all finite length strings (called words). Satisfiability. (SAT) Problems. Given a propositional Boolean formula . φ. (a . ∨ b) ∧ (. a . → b) ∧ (. a . ← b) ∧ ¬ (. a . ∧ b). determine whether a . satisfying assignment . of variables to. and SAT Solvers. SAV, March 18. th. , 2015. Boolean Satisfiability. Goal: find a model that satisfies a propositional formula.. The original NP-complete problem.. “As hard as any other problem in NP.”. Goal: . Show . how . propositional equivalences . are established . & introduce . the most . important such . equivalences.. Copyright © Peter . Cappello. 2. Equivalence. Name. p .  T . ≡ p; p . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Rodrigo de Salvo Braz. Ciaran O’Reilly. Artificial Intelligence Center - SRI International. Vibhav Gogate. University of Texas at Dallas. Rina Dechter. University of California, Irvine. IJCAI-16. , . 1. Boolean Data Lesson #2 Outline. Relational Operations #1. Relational Operations #2. Relational Expressions Example #1. Relational Expressions Example #2. Structure of Boolean Expressions. Boolean Expressions with Parentheses. is a set . B. of values together with: . - two binary operations, commonly denoted by and ∙ , . - a unary operation, usually denoted by . ˉ or ~ or . ’. ,. - two elements usually called . Chapter 2. Basic Definitions. Boolean Algebra defined with a set of elements, a set of operators and a number of . axioms . or postulates.. A set if a collection of objects having a common property. Elements. Karem A. Sakallah. EECS Department. University of Michigan. João Marques Silva. Informatics Department. Technical University of Lisbon. IST/INESC, CEL. SAT tutorial. 2. Context. SAT is the quintessential NP-complete problem. Algebra. Huntington’s Postulates. Truth Tables. Graphic Symbols. Boolean Algebra Theorems. 1. Boolean . Algebra. 2. Boolean . Algebra. A fire sprinkler system should spray water if high heat is sensed and the system is set to . Joseph Busch and Vivian Bliss. Agenda. Pre-defined Boolean Queries. Case Study. Lessons Learned. Boolean queries. Basic operators . AND (conjunctive). OR (disjunctive). NOT (negation). Venn diagrams. Modulo Theories . Manchester 2009. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Modulo Theories. PSpace. -complete. (QBF). Undecidable. (First-order logic).