Splitting the Control Flow with Boolean Flags
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Theoretical Computer Science
Exact join detection for convex polyhedra and other numerical abstractions
Computational Geometry: Theory and Applications
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Note on the Inversion Join for Polyhedral Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
Speeding up Polyhedral Analysis by Identifying Common Constraints
Electronic Notes in Theoretical Computer Science (ENTCS)
Widening polyhedra with landmarks
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
From hybrid data-flow languages to hybrid automata: a complete translation
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Donut domains: efficient non-convex domains for abstract interpretation
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
A new look at the automatic synthesis of linear ranking functions
Information and Computation
Tracking differentiable trajectories across polyhedra boundaries
Proceedings of the 16th international conference on Hybrid systems: computation and control
Complexity analysis of continuous Petri nets
PETRI NETS'13 Proceedings of the 34th international conference on Application and Theory of Petri Nets and Concurrency
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Since the seminal work of Cousot and Halbwachs, the domain of convex polyhedra has been employed in several systems for the analysis and verification of hardware and software components. Although most implementations of the polyhedral operations assume that the polyhedra are topologically closed (i.e., all the constraints defining them are non-strict), several analyzers and verifiers need to compute on a domain of convex polyhedra that are not necessarily closed (NNC). The usual approach to implementing NNC polyhedra is to embed them into closed polyhedra in a higher dimensional vector space and reuse the tools and techniques already available for closed polyhedra. In this work we highlight and discuss the issues underlying such an embedding for those implementations that are based on the double description method, where a polyhedron may be described by a system of linear constraints or by a system of generating rays and points. Two major achievements are the definition of a theoretically clean, high-level user interface and the specification of an efficient procedure for removing redundancies from the descriptions of NNC polyhedra.