Logic Engines as a Service Leonardo de Moura and Nikolaj Bjørner Microsoft Research.

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Presentation transcript:

Logic Engines as a Service Leonardo de Moura and Nikolaj Bjørner Microsoft Research

Satisfiability unsat, Proof Is execution path P feasible? Is assertion X violated? SAGE Is Formula F Satisfiable? WITNESSWITNESS WITNESSWITNESS Solution/Model

Z3 is a collection of Symbolic Reasoning Engines DPLL Simplex Rewriting Superposition Congruence Closure Congruence Closure Groebner Basis Groebner Basis  elimination  elimination Euclidean Solver Euclidean Solver Theorem Prover

Symbolic Reasoning Engine Test Case GenerationVerifying Compilers Model Based Testing Invariant Generation Type Checking Model Checking

Some Applications at Microsoft HAVOC SAGE Vigilante

Impact Used by many research groups TACAS paper (> 1500 citations) More than 35k downloads Ships with many popular systems Isabelle, Pex, SLAM/SDV, … Solved more than 5 Billion constraints created by SAGE when checking Win8 and Office.

Results and Contributions AlgorithmsDecidable Fragments Heuristics

Recent Progress Arithmetic, Bit-Vectors, Booleans, Arrays, Datatypes, Quantifiers New Engines 1. Interpolants 2. Fixed Points 3. Strings 4.Nonlinear arith. Beyond Satisfiability

SMT solvers are popular

Future Z3 with objective functions (Bjørner) Leverage progress in MaxSAT for SMT Stochastic Local Search in Z3 (Wintersteiger) For hard feasibility problems from symbolic execution, floating points Lean: new theorem prover (de Moura) Powerful Dependent Type system, Higher-Order