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Advancements in Logic Engines as a Service: Insights from Microsoft Research

This document explores the cutting-edge developments in symbolic reasoning engines, primarily focusing on the work of Leonardo de Moura and Nikolaj Bjørner of Microsoft Research. It covers various concepts such as satisfiability, theorem proving, model checking, and the application of algorithms in solving complex constraints. Techniques like DPLL, superposition, and congruence closure are discussed alongside practical applications in systems like Windows and Office. The document highlights significant contributions, ongoing research, and future directions in the field of SMT solvers and their extensions.

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Advancements in Logic Engines as a Service: Insights from Microsoft Research

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

  2. Satisfiability Solution/Model sat, unsat, Proof Is execution path P feasible? Is assertion X violated? WI TNESS SAGE Is Formula FSatisfiable?

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

  4. Symbolic Reasoning Engine Test Case Generation Verifying Compilers Model Based Testing Invariant Generation Type Checking Model Checking

  5. Some Applications at Microsoft SAGE HAVOC Vigilante

  6. 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.

  7. Results and Contributions Algorithms Decidable Fragments Data structures Heuristics

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

  9. SMT solvers are popular

  10. Future Z3 with objective functions (Bjørner) Leverage progress in MaxSATfor 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

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