Entity grammar systems: a grammatical tool for studying the hierarchical structures of biological systems.

The hierarchical structures of biological systems are the typical complex hierarchical dynamical structures in the physical world, the effective investigations on which could not be performed with the existing formal grammar systems. To meet the needs of the investigation on these kinds of systems, especially the emerging field of system biology, a grammatical tool was proposed in the present article. Because the grammatical tool mainly deals with the systems composed of structured entities, they are called entity grammar systems (EGSs). The structure of entities in EGSs have the general form of the objects in the physical world, which means EGSs could be used as a tool to study the complex system composed of many objects with different structures, just like the biological systems. The article contains the formal definition of EGSs and the hierarchy of EGSs, which is congruent with the Chomsky hierarchy. The relationship between EGSs and array grammar systems, graph grammar systems, tree grammar systems, multi-set grammar systems are discussed to show the generative power of EGSs. At the end of the present article, the steps to define new grammar systems with the form of EGS are provided and the possible applicable fields of EGSs are discussed.