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Logic Engines as a Service. Leonardo de Moura and Nikolaj Bjørner Microsoft Research. Satisfiability. Solution/Model. s at, . unsat , P roof. Is execution path P feasible?. Is assertion X violated?. WI TNESS. SAGE. Is Formula F Satisfiable ?. Theorem Prover. Simplex.

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Logic engines as a service

Logic Engines as a Service

Leonardo de Moura and Nikolaj Bjørner

Microsoft Research


Satisfiability
Satisfiability

Solution/Model

sat,

unsat, Proof

Is execution path P feasible?

Is assertion X violated?

WI

TNESS

SAGE

Is Formula FSatisfiable?


Theorem Prover

Simplex

Rewriting

DPLL

Superposition

Z3 is a collection of

Symbolic Reasoning Engines

Congruence

Closure

Euclidean

Solver

Groebner

Basis



elimination


Symbolic reasoning engine
Symbolic Reasoning Engine

Test Case Generation

Verifying Compilers

Model Based Testing

Invariant Generation

Type Checking

Model Checking


Some applications at microsoft
Some Applications at Microsoft

SAGE

HAVOC

Vigilante


Impact
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
Results and Contributions

Algorithms

Decidable Fragments

Data structures

Heuristics


Recent progress
Recent Progress

1. Interpolants

2. Fixed Points

Beyond

Satisfiability

Arithmetic, Bit-Vectors,

Booleans, Arrays,

Datatypes, Quantifiers

New Engines

3. Strings

4.Nonlinear arith.



Future
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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