Scalable Analysis of Linear Systems Using Mathematical Programming

  title={Scalable Analysis of Linear Systems Using Mathematical Programming},
  author={Sriram Sankaranarayanan and Henny B. Sipma and Zohar Manna},
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… 
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Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear
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