Algorithm for detection of algebraic Bayesian network primary structure acyclicity based on its quaternary structure

Algebraic Bayesian networks (ABN) belong to a class of logical and probabilistic graphical models of systems of knowledge with uncertainty. ABN allows to use interval probability estimates to represent uncertainty in knowledge. One of the most important conditions for ABN performance capability is the absence of cycles in its secondary structure. The primary structure, on which an acyclic ABN can be synthesized, is called acyclic primary structure. The goal of the work is to propose an algorithm for detection of the primary structure acyclicity on the basis of analysis of the quaternary structure of the ABN, as well as evaluation of the algorithm complexity. The algorithm for acyclicity detection is formulated, its correctness is proven, its complexity is estimated and a number of improvements for the acceleration of this algorithm are proposed.