Static analysis of logic programs for independent and parallelism
Journal of Logic Programming
Complementation in abstract interpretation
ACM Transactions on Programming Languages and Systems (TOPLAS)
The quotient of an abstract interpretation
Theoretical Computer Science
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Complete Abstract Interpretations Made Constructive
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Completeness in Abstract Interpretation: A Domain Perspective
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
Factorizing Equivalent Variable Pairs in ROBDD-Based Implementations of Pos
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
The Boolean Logic of Set Sharing Analysis
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative Programming
Complementation in Abstract Interpretation
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Set-Sharing is Redundant for Pair-Sharing
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
The Correctness of Set-Sharing
SAS '98 Proceedings of the 5th International Symposium on Static Analysis
Set-sharing is redundant for pair-sharing
Theoretical Computer Science
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Complementation, the inverse of the reduced product operation, is a relatively new technique for systematically finding minimal decompositions of abstract domains. FilÉ and Ranzato advanced the state of the art by introducing a simple method for computing a complement. As an application, they considered the extraction by complementation of the pair-sharing domain PS from the Jacobs and Langen's set-sharing domain SH. However, since the result of this operation was still SH, they concluded that PS was too abstract for this. Here, we show that the source of this difficulty lies not with PS but with SH and, more precisely, with the redundant information contained in SH with respect to ground-dependencies and pair-sharing. In fact, the difficulties vanish if our non-redundant version of SH, SHρ, is substituted for SH. To establish the results for SHρ, we define a general schema for subdomains of SH that includes SHρ and Def as special cases. This sheds new light on the structure of SHρ and exposes a natural though unexpected connection between Def and SHρ. Moreover, we substantiate the claim that complementation alone is not sufficient to obtain truly minimal decompositions of domains. The right solution to this problem is to first remove redundancies by computing the quotient of the domain with respect to the observable behavior, and only then decompose it by complementation.