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# Logic Engines as a Service PowerPoint PPT Presentation

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.

Logic Engines as a Service

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## Logic Engines as a Service

Leonardo de Moura and Nikolaj Bjørner

Microsoft Research

### 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

Test Case Generation

Verifying Compilers

Model Based Testing

Invariant Generation

Type Checking

Model Checking

SAGE

HAVOC

Vigilante

### Impact

Used by many research groups

TACAS paper (> 1500 citations)

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

Algorithms

Decidable Fragments

Data structures

Heuristics

### Recent Progress

1. Interpolants

2. Fixed Points

Beyond

Satisfiability

Arithmetic, Bit-Vectors,

Booleans, Arrays,

Datatypes, Quantifiers

New Engines

3. Strings

4.Nonlinear arith.

### 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