Abstract
We discuss two non-standard models of nonadaptive combinatorial search which develop the conventional disjunct search model for a small number of defective elements contained in a finite ground set or a population. The first model is called a search of defective supersets. The second model is called a search of defective subsets in the presence of inhibitors. For these models, we study the constructive search methods based on the known constructions for the disjunct model.
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