# Scalable Analysis of Linear Systems Using Mathematical Programming

@inproceedings{Sankaranarayanan2005ScalableAO, title={Scalable Analysis of Linear Systems Using Mathematical Programming}, author={Sriram Sankaranarayanan and Henny B. Sipma and Zohar Manna}, booktitle={VMCAI}, year={2005} }

We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The number and dimensionality of the LP queries are polynomial in the program dimensionality, size and the…

## 224 Citations

Polyhedron over-approximation for complexity reduction in static analysis

- Computer ScienceInt. J. Comput. Math. Comput. Syst. Theory
- 2018

ABSTRACT Polyhedra are widely used in the verification of numerical programs. Specially, in the field of static analysis by abstract interpretation to express the program invariants. Polyhedra make…

Solving systems of rational equations through strategy iteration

- Computer ScienceTOPL
- 2011

The present article applies techniques for computing abstract least fixpoint semantics of affine programs over the relational template polyhedra domain to practical algorithms for computing exact least solutions of equation systems over the reals with addition, multiplication by positive constants, minimum and maximum.

The Gauge Domain: Scalable Analysis of Linear Inequality Invariants

- Computer ScienceCAV
- 2012

The gauge domain is introduced, which enables the efficient inference of general linear inequality invariants within loops within loops, and is demonstrated on a real 144K LOC intelligent flight control system, which implements advanced adaptive avionics.

A scalable algebraic method to infer quadratic invariants of switched systems

- Mathematics, Computer Science2015 International Conference on Embedded Software (EMSOFT)
- 2015

A fast non-linear power-type algorithm is developed, which allows one to determine sound quadratic invariants on switched systems in a tractable way, by solving fixed point problems over the space of ellipsoids.

Efficient Strongly Relational Polyhedral Analysis

- Computer ScienceVMCAI
- 2006

This work proposes a polynomial time approach to strongly relational analysis of polyhedra analysis, and provides efficient implementations of join and post condition operations, achieving a trade off between performance and accuracy.

Abstract Acceleration in Linear relation analysis (extended version)

- Computer Science
- 2013

This research report gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives.

A Sound Floating-Point Polyhedra Abstract Domain

- Computer ScienceAPLAS
- 2008

This is the first time that the polyhedra domain is adapted to floating-point arithmetic in a sound way and the preliminary experimental results of the prototype are encouraging.

Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion

- Mathematics, Computer ScienceCAV
- 2009

A new algorithm for over-approximating such images based on the Bernstein expansion of polynomial functions is proposed, which was demonstrated on two practical systems as well as a number of randomly generated examples.

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