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Scalable Analysis of Linear Systems Using Mathematical Programming

  • Sriram Sankaranarayanan
  • Henny B. Sipma
  • Zohar Manna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3385)

Abstract

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 number of target invariants. The method generalizes similar analyses in the interval, octagon, and octahedra domains, without resorting to polyhedral manipulations. We demonstrate the performance of our method on some benchmark programs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sriram Sankaranarayanan
    • 1
  • Henny B. Sipma
    • 1
  • Zohar Manna
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

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