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PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
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RTSS '97 Proceedings of the 18th IEEE Real-Time Systems Symposium
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Dynamic Programming
Precise and efficient static array bound checking for large embedded C programs
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Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Higher-Order and Symbolic Computation
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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)
Fast decision algorithms based on union and find
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of 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
Polynomial time array dataflow analysis
LCPC'01 Proceedings of the 14th international conference on Languages and compilers for parallel computing
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
ESOP'05 Proceedings of the 14th European conference on Programming Languages and 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
Loop refinement using octagons and satisfiability
SSV'10 Proceedings of the 5th international conference on Systems software verification
Transfer function synthesis without quantifier elimination
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
A new look at the automatic synthesis of linear ranking functions
Information and Computation
Access-Based Localization for Octagons
Electronic Notes in Theoretical Computer Science (ENTCS)
Sub-polyhedral scheduling using (unit-)two-variable-per-inequality polyhedra
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Weakly-relational numeric constraints provide a compromise between complexity and expressivity that is adequate for several applications in the field of formal analysis and verification of software and hardware systems. We address the problems to be solved for the construction of full-fledged, efficient and provably correct abstract domains based on such constraints. We first propose to work with semantic abstract domains, whose elements are geometric shapes, instead of the (more concrete) syntactic abstract domains of constraint networks and matrices on which the previous proposals are based. This allows to solve, once and for all, the problem whereby closure by entailment, a crucial operation for the realization of such domains, seemed to impede the realization of proper widening operators. In our approach, the implementation of widenings relies on the availability of an effective reduction procedure for the considered constraint description: one for the domain of bounded difference shapes already exists in the literature; we provide algorithms for the significantly more complex cases of rational and integer octagonal shapes. We also improve upon the state-of-the-art by presenting, along with their proof of correctness, closure by entailment algorithms of reduced complexity for domains based on rational and integer octagonal constraints. The consequences of implementing weakly-relational numerical domains with floating point numbers are also discussed.