A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
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
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
Higher-Order and Symbolic Computation
Widening operators for powerset domains
International Journal on Software Tools for Technology Transfer (STTT)
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Pentagons: a weakly relational abstract domain for the efficient validation of array accesses
Proceedings of the 2008 ACM symposium on Applied computing
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Relational Abstract Domain of Weighted Hexagons
Electronic Notes in Theoretical Computer Science (ENTCS)
Quadtrees as an Abstract Domain
Electronic Notes in Theoretical Computer Science (ENTCS)
BOXES: a symbolic abstract domain of boxes
SAS'10 Proceedings of the 17th international conference on Static analysis
Static analysis in disjunctive numerical domains
SAS'06 Proceedings of the 13th international conference on Static Analysis
Trace partitioning in abstract interpretation based static analyzers
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
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In this paper we present how sweeping line techniques, which are very popular in computational geometry, can be adapted for static analysis of computer software by abstract interpretation. We expose how concept of the sweeping line can be used to represent elements of a numerical abstract domain of boxes, which is a disjunctive refinement of a well known domain of intervals that allows finite number of disjunctions. We provide a detailed description of the representation along with standard domain operations algorithms. Furthermore we introduce very precise widening operator for the domain. Additionally we show that the presented idea of the representation based on sweeping line technique is a generalisation of the representation that uses Linear Decision Diagrams (LDD), which is one of possible optimisations of our idea. We also show that the presented widening operator is often more precise than the previous one.