PPT-Lazy Proofs for DPLL(T)-Based SMT Solvers

Guy Katz Schloss Dagstuhl October 2016 Acknowledgements Based on joint work with Clark Barrett Cesare Tinelli Andrew Reynolds and Liana Hadarean FMCAD16 2 Stanford University. CSeq. :. A . Lazy . Sequentialization. Tool for . C. Omar . Inverso. University of Southampton, UK. Ermenegildo. . Tomasco. University of Southampton, UK. Bernd Fischer. Stellenbosch University, South Africa. Program Analysis and Verification . Nikolaj Bj. ø. rner. Microsoft Research. Lecture 5. Overview of the lectures. Day. Topics. Lab. 1. Overview of SMT and applications. . SAT solving part I.. Program exploration with Pex. Yeting. . Ge. Clark Barrett. SMT . 2008. July 7 Princeton. SMT solvers are more complicated. CVC3 contains over 100,000 lines of code. Are SMT solvers correct?. . Quest for . correct. SMT solvers?. Andrew Reynolds. Cesare. . Tinelli. Leonardo De . Moura. July 18, 2014. Outline of Talk. SMT solvers:. . Efficient. methods for . ground. constraints. . Heuristic. methods for . quantified. formulas. Andrew Reynolds. March 18, 2015. Overview. SAT : Satisfiability for Propositional Logic. ( A .  B )  ( C  D )  B. Does there exist truth values for A, B, C, D that make this formula true?. First points:. This is written for mathematical proofs. Unless you are doing math econ, formal game theory, or statistical/econometric development (not application) you may not do formal mathematical proofs.. DPLL(T)-Based SMT Solvers. Guy . Katz. , Clark Barrett, . Cesare . Tinelli. , Andrew Reynolds, Liana . Hadarean. Stanford . University. The University. of Iowa. Synopsys. Producing Checkable Artifacts. A Tutorial. Nikolaj Bjørner . Microsoft Research. Dagstuhl . April 23, 2015. Plan. SMT in a nutshell. SMT solving walkthrough by example. Selected Theory solvers. Equalities. Arrays. Arithmetic. Combining Solvers. 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. We wish to establish the truth of. Procedures. Conclusions. Future Work. Objectives. Results. Research Undergraduate:. Joshua Walters. Advisor:. Dr. Michael West. Impact. Acknowledgements:. Thanks to the National Science Foundation grant # 0852057 . VS Experiments 2008 . –. Toronto, Canada. Leonardo de Moura. Microsoft Research. Agenda. What is SMT?. Experiments:. Windows kernel verification.. Extending SMT solvers.. Garbage collector (Singularity) verification. The quick brown fox jumps over the lazy dog. The quick brown fox jumps over the lazy dog. The quick brown fox jumps over the lazy dog. The quick brown fox jumps over the lazy dog. The quick brown fox jumps over the lazy dog. . Jaideep. . Nijjar. . Tevfik Bultan. University of California, Santa Barbara. ASE 2012. Web . Software Everywhere. Commerce, entertainment, social interaction. We will rely on web apps more in the future. Sriram Rajamani. (based on notes/slides by Matt Fredrickson, Andre . Platzer. , . Emina Torlak and Leonardo . De Moura). Modern SAT solvers. First convert a formula to CNF (Conjunctive Normal Form). Use variant of DPLL (Davis Putnam .