A hypergraph is a generalized structure of a graph in which an edge, called a hyperedge, can have more than two vertices. A subset *T* is said to be a transversal of a given hypergraph if it intersects every (non-empty) set of vertices in the hypergraph. A hypergraph is called an exact transversal hypergraph (*xt*-hypergraph) if every transversal of it is an exact transversal.

In the paper, Eiter first proposes an algorithm for *xt*-hypergraph recognition and establishes that recognizing *xt*-hypergraphs can be done in polynomial time with a runtime bounded by *O*(*mS*^{2}), where *m* is the order of the hypergraph concerned and *S* is the input size. Following this, he proposes an algorithm to generate minimal transversals of a hypergraph and proves that the minimal traversals of an *xt*-hypergraph can be obtained in inverse lexicographic order with a delay of *O*(*nS*), and hence the maximal independent set can be obtained in lexicographic order with a delay of *O*(*nS*).

In the second half of the paper, the author describes some applications of the study to Boolean μ-functions. Let *f*_{E} be a Boolean function corresponding to a monotone Boolean expression *E* in conjunctive normal form (CNF) or disjunctive normal form (DNF). The first theorem of the section states that deciding whether the function *f*_{E} is μ-equivalent is possible in *n*^{2}*m*^{3}, where *m* is the number of clauses of *E*. It is also proved that deciding whether a Boolean function *f*_{E} corresponding to a monotone Boolean expression *E* is a μ-function is co-NP-complete. As the final result of the paper, the author establishes that the prime implicants of the dual of an *n*-ary monotone μ-function *f* can be generated in lexicographic order with a delay of *O*(*nS*), provided the prime implicants of *f* are given.

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