Geodesic
Reliability of binary systems
Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 129-139
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The main result of the paper is a theorem characterizing the combinatorial structure of pathsets and cutsets of regular binary systems. As direct corollaries of the theorem the following results are presented: efficient algorithms for computing the reliability and determining all minimal cutsets of regular and uniform regular systems are given; a constructive characterization of regular systems having a matroidal structure is suggested; efficiently computable lower bounds for the reliability of uniform systems, which are provided by regular systems, are obtained. 
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A. A. Chernyak; Zh. A. Chernyak. Reliability of binary systems. Diskretnaya Matematika, Tome 11 (1999) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/DM_1999_11_1_a8/