Grids: a domain for analyzing the distribution of numerical values

Authors:
Roberto Bagnara;Katy Dobson;Patricia M. Hill;Matthew Mundell;Enea Zaffanella
Affiliations:
Department of Mathematics, University of Parma, Italy;School of Computing, University of Leeds, UK;School of Computing, University of Leeds, UK;School of Computing, University of Leeds, UK;Department of Mathematics, University of Parma, Italy
Venue:
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Year:
2006

Citing 14
Cited 11

Theory of linear and integer programming

Theory of linear and integer programming
Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
Static analysis of linear congruence equalities among variables of a program

TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
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
Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Increasing and Detecting Memory Address Congruence

Proceedings of the 2002 International Conference on Parallel Architectures and Compilation Techniques
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation

PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library

SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Static Analyses of Congruence Properties on Rational Numbers (Extended Abstract)

SAS '97 Proceedings of the 4th International Symposium on Static Analysis
A Few Graph-Based Relational Numerical Abstract Domains

SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Precise interprocedural analysis through linear algebra

Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Widening operators for powerset domains

International Journal on Software Tools for Technology Transfer (STTT) - A View from Formal Methods 2003 (pp 301-354); Special Section on Recent Advances in Hardware Verification (pp 355-447)
Analysis of modular arithmetic

ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
A generic framework for interprocedural analysis of numerical properties

SAS'05 Proceedings of the 12th international conference on Static Analysis

The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems

Science of Computer Programming
Inferring Congruence Equations Using SAT

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Applications of polyhedral computations to the analysis and verification of hardware and software systems

Theoretical Computer Science
An improved tight closure algorithm for integer octagonal constraints

VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Quadtrees as an Abstract Domain

Electronic Notes in Theoretical Computer Science (ENTCS)
Range analysis of microcontroller code using bit-level congruences

FMICS'10 Proceedings of the 15th international conference on Formal methods for industrial critical systems
Probabilistic abstractions with arbitrary domains

SAS'11 Proceedings of the 18th international conference on Static analysis
Automatic abstraction for congruences

VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Applying abstract acceleration to (co-)reachability analysis of reactive programs

Journal of Symbolic Computation
Taming the wrapping of integer arithmetic

SAS'07 Proceedings of the 14th international conference on Static Analysis
Abstract interpretation of microcontroller code: Intervals meet congruences

Science of Computer Programming

Quantified Score

Hi-index	0.01

Visualization

Abstract

This paper explores the abstract domain of grids, a domain that is able to represent sets of equally spaced points and hyperplanes over an n-dimensional vector space. Such a domain is useful for the static analysis of the patterns of distribution of the values program variables can take. We present the domain, its representation and the basic operations on grids necessary to define the abstract semantics. We show how the definition of the domain and its operations exploit well-known techniques from linear algebra as well as a dual representation that allows, among other things, for a concise and efficient implementation.