The octahedron abstract domain

An interesting area in static analysis is the study of numerical properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numerical abstract domain called octahedron that represents constraints of the form (∑xi−∑xj≥k). The implementation of octahedra is based on a new kind of decision diagram called Octahedron Decision Diagrams (OhDD).