Algebraic specification of graph computational structures

Problems of composing algebraic specifications for computational structures represented by data flow graphs are considered. The evolution of algebraic program specification tools is briefly outlined, from many-sorted algebra via coalgebra to a category-theoretical construction of dialgebra capable of describing interactive computing nodes. As a next step, a novel category-theoretical construction called graphalgebra is proposed which allows combining dialgebras into arbitrary directed multigraphs whose edges represent computational operations at nodes and whose vertices describe data exchanged between nodes. Examples of graphalgebraic specifications for neural networks and multiprocessor computational systems are given. The method of building categories of graphalgebras via universal constructions is described. For a computational structure of the system of systems kind consisting of graph structures, methods of hierarchical construction of an algebraic specification from the specifications of components are proposed.