Logical-Probabilistic Models of Complex Systems Constructed on the Modular Principle and Their Reliability

摘要

The aim of this paper is to define a system built on a modular principle and to construct a recursive algorithm for calculating its reliability. For this purpose, the system is described using a monotone Boolean function that characterizes its performance. The oriented tree is mapped to a Boolean function (which characterizes operability). From any leaf of this tree there is a (single) path to its root. We assume that all the edges of this path are directed towards the root. A recursive algorithm for calculating the Boolean function and the reliability of the system, described by this function, is constructed. It is proved that the number of arithmetic operations for calculating a Boolean function, built on the modular principle, and the reliability of the system depend linearly on the number of leaves in the tree. Then how for systems of general form of this dependence is exponential.