Implicit Boolean networks and their application to combinatorial problems

Abstract

For implicit binary dynamical systems of the \textit{k}-th order with a given initial state, a new approach based on the Boolean constraints method is developed for constructing local trajectories that ensure the achievement of a given value of the objective function on these trajectories. A specialized algorithm is proposed for solving the Boolean satisfiability problem using deep parallelization. It provides scalability with an increase in the dimension of the state vector of an implicit system and the length of its local trajectories. An implicit Boolean model is constructed for solving the problem of minimum set coverage, and some results of computational experiments for this model are presented.