The Abstract Domain of Parallelotopes
نویسندگان
چکیده
We propose a numerical abstract domain based on parallelotopes. A parallelotope is a polyhedron whose constraint matrix is squared and invertible. The domain of parallelotopes is a fully relational abstraction of the Cousot and Halbwachs’ polyhedra abstract domain, and does not use templates. We equip the domain of parallelotopes with all the necessary operations for the analysis of imperative programs, and show optimality results for the abstract operators.
منابع مشابه
Random: R-Based Analyzer for Numerical Domains
We present the tool Random (R-based Analyzer for Numerical DOMains) for static analysis of imperative programs. The tool is based on the theory of abstract interpretation and implements several abstract domains for detecting numerical properties, in particular integer loop invariants. The tool combines a statistical dynamic analysis with a static analysis on the new domain of parallelotopes. Th...
متن کاملProperties of parallelotopes equivalent to Voronoi's conjecture
A parallelotope is a polytope whose translation copies fill space without gaps and intersections by interior points. Voronoi conjectured that each parallelotope is an affine image of the Dirichlet domain of a lattice, which is a Voronoi polytope. We give several properties of a parallelotope and prove that each of them is equivalent to it is an affine image of a Voronoi polytope.
متن کاملA Tool Which Mines Partial Execution Traces to Improve Static Analysis
We present a tool which performs abstract interpretation based static analysis of numerical variables. The novelty is that the analysis is parametric, and parameters are chosen by applying a variant of principal component analysis to partial execution traces of programs. Abstract interpretation based static analysis [5] may be used to prove runtime properties of program variables such as “all t...
متن کاملAnalysis of disassembled executable codes by abstract interpretation
The aim of this paper is to dene the abstract domain, abstract operator, abstract semantic, the environments and states of disassembled executable codes as well as a way to analysis the disassembled executable codes. Nowadays, static analysis on disassembled code going to grow. Reverse engineering and malware analysis use this technique. Thus, we tried to perform pluralization the requirements ...
متن کاملNumerical quadrature for high-dimensional singular integrals over parallelotopes
We introduce and analyze a family of algorithms for an efficient numerical approximation of integrals of the form I = ∫ C(1) ∫ C(2) F (x, y, y−x)dydx where C, C are d-dimensional parallelotopes (i.e. affine images of d-hypercubes) and F has a singularity at y − x = 0. Such integrals appear in Galerkin discretization of integral operators in R. We construct a family of quadrature rules QN with N...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 287 شماره
صفحات -
تاریخ انتشار 2012