Fast Numerical Abstract Domains

In this project we develop optimized implementations of popular numerical abstract domains such as Polyhedra, Octagon and Zonotopess for static analysis of programs and neural networks. We design improved algorithms, online decomposition as well as performance optimizations from linear algebra such as vectorization, locality of reference, scalar replacement etc. to significantly improve the performance of numerical domains.

Systems

ELINA: ETH Library for Numerical Analysis

ELINA contains optimized implementations of popular numerical abstract domains such as Polyhedra, Octagon and Zones

Publications

2020

Learning Fast and Precise Numerical Analysis

Jingxuan He, Gagandeep Singh, Markus Püschel, Martin Vechev

PLDI 2020

Slides
Talk
Paper
Code

2018

Fast Numerical Program Analysis with Reinforcement Learning

Gagandeep Singh, Markus Püschel, Martin Vechev

CAV 2018

Slides
Paper

A Practical Construction for Decomposing Numerical Abstract Domains

Gagandeep Singh, Markus Püschel, Martin Vechev

ACM POPL 2018

Slides
Talk
Paper

2017

Fast Polyhedra Abstract Domain

Gagandeep Singh, Markus Püschel, Martin Vechev

ACM POPL 2017

Slides
Talk
Paper

2015

Making Numerical Program Analysis Fast

Gagandeep Singh, Markus Püschel, Martin Vechev

ACM PLDI 2015

Slides
Paper