Coordination of parallel partially ordered processes

Isomorphic representations of finite distributive lattices by lattices of functions and fuzzy sets are constructed. These class es the case of finite lattices are the generalization of the representation of distributive lattices by set lattices whose existence is proved by Birkhoff’s theorem. Homomorphic image and subdirect representations of finite distributive lattices are characterized, and figure of two-dimensional distributive lattices are geometrically characterized. This theoretical basis underlies the general description of systems of linear and partially ordered parallel discrete processes with mutual constraints on step order acting between them. The application of the developed tools is demonstrated on the examples from the graph theory, parallel calculations, artificial intelligence, and power engineering.