Series of graphs generated by rational machines
Developmental process of a multi-cellular organism is considered as a series of graphs, whose nodes correspond to cells and edges to cellular interconnections. We introduce a new machinary, called rational machine, for generating series of finite directed graphs. From the biological motivation, each node is named with a string of symbols. At first, the growth rate of graphs is analyzed. The generative capability of rational machines is shown by giving many examples. Decision problems and closure properties under graph operations are also discussed. Among others it is shown that whether two rational machines generate the same series of graphs is undecidable.
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