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Call an hypergraph, that is a family of subsets (edges) from afinite vertex set, an exact transversal hypergraph iff each of itsminimal traversals, i.e., minimal vertex subsets that intersect eachedge, meets each edge in a singleton. We show that such hypergraphs arerecognizable in polynomial time and that their minimal transversals aswell as their maximal independent sets can be generated in lexicographicorder with polynomial delay between subsequent outputs, which isimpossible in the general case unlessP=NP. The results obtained are applied tomonotone Boolean &mgr;-functions, that are Boolean functions defined bya monotone Boolean expression (that is, built with ∧,∨ only) in which no variable occurs repeatedly. We alsoshow that recognizing such functions from monotone Boolean expressionsis co-NP-hard, thus complementingMundici's result that this problem is inco-NP.—Author's Abstract