Making abstract interpretations complete
Journal of the ACM (JACM)
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 complexity of checking consistency of pedigree information and related problems
Journal of Computer Science and Technology - Special issue on bioinformatics
Finding Consistent Gene Transmission Patterns on Large and Complex Pedigrees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Generalizing the Paige--Tarjan algorithm by abstract interpretation
Information and Computation
A forward-backward abstraction refinement algorithm
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Efficient Genotype Elimination via Adaptive Allele Consolidation
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We apply Abstract Interpretation to the problem of genotype elimination in pedigrees. First, we give a formalization of some existing algorithms that try to remove from pedigrees all genotypes that violate the Mendelian rules of inheritance. The formalization enables the application of the Abstract Interpretation technique to the problem. We then introduce a particular abstraction, parameterized on given partitions of the set of genotypes. We instantiate this abstraction in order to obtain two existing algorithms for Allele Consolidation, thus giving a formal proof of their correctness. Moreover, the second of these two algorithms is shown to be an example of a forward complete abstraction.