A technique for summarizing data access and its use in parallelism enhancing transformations
PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Handbook of logic in computer science (vol. 3)
A hierarchy of constraint systems for data-flow analysis of constraint logic-based languages
Science of Computer Programming - Special issue on concurrent constraint programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computational Geometry: Theory and Applications
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The Modulo Interval: A Simple and Practical Representation for Program Analysis
PACT '99 Proceedings of the 1999 International Conference on Parallel Architectures and Compilation Techniques
Efficient verification of real-time systems: compact data structure and state-space reduction
RTSS '97 Proceedings of the 18th IEEE Real-Time Systems Symposium
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Code Generation in the Polyhedral Model Is Easier Than You Think
Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Verifying analog oscillator circuits using forward/backward abstraction refinement
Proceedings of the conference on Design, automation and test in Europe: Proceedings
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)
Widening operators for powerset domains
International Journal on Software Tools for Technology Transfer (STTT)
Executable Analysis using Abstract Interpretation with Circular Linear Progressions
MEMOCODE '07 Proceedings of the 5th IEEE/ACM International Conference on Formal Methods and Models for Codesign
Pentagons: a weakly relational abstract domain for the efficient validation of array accesses
Proceedings of the 2008 ACM symposium on Applied computing
Value-Range Analysis of C Programs: Towards Proving the Absence of Buffer Overflow Vulnerabilities
Value-Range Analysis of C Programs: Towards Proving the Absence of Buffer Overflow Vulnerabilities
Theoretical Computer Science
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Symbolic model checking of hybrid systems using template polyhedra
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Widening operators for weakly-relational numeric abstractions
SAS'05 Proceedings of the 12th international conference on Static Analysis
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
isl: an integer set library for the polyhedral model
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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
An abstract domain to infer types over zones in spreadsheets
SAS'12 Proceedings of the 19th international conference on Static Analysis
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Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification and optimization of hardware and software systems. In such application fields though, general convex polyhedra are just one among many, so-called, numerical abstractions, which range from restricted families of (not necessarily closed) convex polyhedra to non-convex geometrical objects. We thus tackle the problem from an abstract point of view: for a wide range of numerical abstractions that can be modeled as bounded join-semilattices-that is, partial orders where any finite set of elements has a least upper bound-we show necessary and sufficient conditions for the equivalence between the lattice-theoretic join and the set-theoretic union. For the case of closed convex polyhedra-which, as far as we know, is the only one already studied in the literature-we improve upon the state-of-the-art by providing a new algorithm with a better worst-case complexity. The results and algorithms presented for the other numerical abstractions are new to this paper. All the algorithms have been implemented, experimentally validated, and made available in the Parma Polyhedra Library.