Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Static Analyses of the Precision of Floating-Point Operations
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A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Safe bounds in linear and mixed-integer linear programming
Mathematical Programming: Series A and B
Field-sensitive value analysis of embedded C programs with union types and pointer arithmetics
Proceedings of the 2006 ACM SIGPLAN/SIGBED conference on Language, compilers, and tool support for embedded systems
Higher-Order and Symbolic Computation
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Exploiting sparsity in polyhedral analysis
SAS'05 Proceedings of the 12th international conference on Static Analysis
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Static analysis for software assurance: soundness, scalability and adaptiveness
Proceedings of the FSE/SDP workshop on Future of software engineering research
A persistent public watermarking of relational databases
ICISS'10 Proceedings of the 6th international conference on Information systems security
Cooperative query answering by abstract interpretation
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Simple and precise widenings for H-polyhedra
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Static contract checking with abstract interpretation
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
Trustworthy numerical computation in Scala
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Cost analysis of object-oriented bytecode programs
Theoretical Computer Science
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Boosting local consistency algorithms over floating-point numbers
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
A formal proof of square root and division elimination in embedded programs
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Counterexample-guided abstraction refinement for linear programs with arrays
Automated Software Engineering
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The polyhedra abstract domain is one of the most powerful and commonly used numerical abstract domains in the field of static program analysis based on abstract interpretation. In this paper, we present an implementation of the polyhedra domain using floating-point arithmetic without sacrificing soundness. Floating-point arithmetic allows a compact memory representation and an efficient implementation on current hardware, at the cost of some loss of precision due to rounding. Our domain is based on a constraint-only representation and employs sound floating-point variants of Fourier-Motzkin elimination and linear programming. The preliminary experimental results of our prototype are encouraging. To our knowledge, this is the first time that the polyhedra domain is adapted to floating-point arithmetic in a sound way.