PARALLEL GRAPH GENERATING AND GRAPH RECURRENCE SYSTEMS FOR MULTICELLULAR DEVELOPMENT

Abstract As an extension of parallel rewriting systems on strings of symbols (L-systems), graph generating systems (graph L-systems) and graph recurrence systems are defined, by which the development of multicellular organisms can be modelled. Organisms are represented by directed graphs with labelled nodes and labeled edges. The nodes stand for cells, their labels for cellular states; the edges for connections between neighbors, their labels and directions for geometric relationships. In generating systems, a new graph is produced by simultaneous substitution of graphs for nodes according to a finite set of production, and by connecting their nodes by adding new edges according to a finite set of connection rules (using “stencils”). In graph recurrence systems larger and larger graphs are defined by recursive formulas on graphs and stencils. Results are given on the hierarchy of graph language families, as well as on some decidability problems concerning them.