Reliability of binary systems

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.