About Time-Varying Distributed H Systems

A time-varying distributed H system (TVDH system) is a splicing system which has the following feature: at different moments one uses different sets of splicing rules (these sets are called components of TVDH system). The number of components is called the degree of the TVDH system. The passing from a component to another one is specified in a cycle. It was proved by both authors (1999) that TVDH systems of degree 2 generate all recursively enumerable languages. It was made by modelling Turing machines and, in that modelling, every language is generated "step by step" or "word by word". This solution is not a fully parallel one. A. Paun (1999) presented a complete parallel solution for TVDH systems of degree 4 by modelling type 0 formal grammars. Now we improved A. Paun's result by reducing the number of components of such TVDH systems down to 3. This question is open for 2 components, i.e. is it possible to construct TVDH systems of degree 2 which completely uses the parallel nature of molecular computations based on splicing operations (say model type 0 formal grammars). We consider also original G. Paun's definition of TVDH systems and suggest a slightly different definition of TVDH systems based on the definition of H systems - extended time-varying distributed H systems (ETVDH systems). For this new definition we proved that ETVDH systems with one component generate exactly the set of all regular languages and that with two components, they generate exactly the set of all recursively enumerable languages.

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