An Abstract Interpretation framework for genotype elimination algorithms

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.