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. The standard method for deciding bitvector constraints is via eager reduction to propositional logic This is usually done after 64257rst applying powerful rewrite techniques While often ef64257cient in practice this method does not scale on problems Lecturer: . Qinsi. Wang. May 2, 2012. Z3. high-performance theorem . prover. being developed at Microsoft Research.. mainly by Leonardo de . Moura. and . Nikolaj. . Bjørner. . . Free (online interface, APIs, …) . Spring 2011. Review. Overview. Course overview. Propositional Logic Example. CSP Example. Hints for Final. Course Review. AI introduction. Agents. Searching. Uninformed. Informed. Local. Adversarial search. Leonardo de Moura and Nikolaj . Bjørner. Microsoft Research. What. EPR . . . Deciding EPR using DPLL + Substitution sets. Why? EPR is the next SAT. SAT .  EPR. Deciding EPR using DPLL + Substitution sets. Terminology. Propositional variable: . boolean. variable (p). Literal: propositional variable or its negation. p . p. Clause: disjunction of literals q \/ . . p \/ . . r. . given by set of . 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. Teaching & Learning Conference. Jane Nolan MBE. Entrepreneur in Residence and Development Officer (Careers Service). Katie Wray. Lecturer in Enterprise (SAgE Faculty). Entrepreneurial Students. Some statistics:. 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. SAT/SMT Summer School 2014. Parallel SAT. Motivation. Technical. Clock frequency has hit the thermal wall. Multicore CPUs to cope with it. Algorithmic. Sequential SAT seems hard to improve . SAT applied to ever harder problems. Richard Peng. Georgia Tech. Based on . recent works . joint with:. Serban . Stan (Yale. ), . Haoran. . Xu (MIT. ),. Shen . Chen Xu (CMU. ), . Saurabh. . Sawlani. (. GaTech. ). John . Gilbert (UCSB. : A Threaded Sparse LU factorization . utilizing Hierarchical Parallelism and Data Layouts. Siva Rajamanickam . Joshua Booth, Heidi . Thornquist. Sixth International Workshop on Accelerators and Hybrid . to Proof Complexity. Paul Beame. University of Washington. Proof . Systems and Their Complexity. 2. 3. NP, proofs, and proof systems. L. ∊. NP. : there is a polynomial time computable . V . s.t.. x . Preprocessing. Can . Efficiently. . Simulate. Resolution. Paul . Beame. *. . Ashish Sabharwal. . *. Computer Science and Engineering, University of Washington, Seattle, WA, USA. . Allen Institute for Artificial Intelligence, Seattle, WA, USA. 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 .