LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

288 Manfred Kudlek
Theorem 16. γRAT(◦) ⊆ γκRAT( ).
Proof. This follows immediately from Theorem 15. ✷
The relations between the language classes considered so far are shown in
the diagrams of Figures 1 and 2.
4 Conclusion
An open problem is whether the inclusions RAT(◦) ⊆ κRAT( ) and
γRAT(◦) ⊆ γκRAT( ) are proper or not. Other problems to be solved are
the relation of language classes defined by grammars on cyclic words to those
language classes considered above, and closure properties under certain language
operations. Also the relations of language classes defined as algebraic closure under
the operations ⊙ and ⊗ have to be investigated. These are related to simple
circular splicing operations [3]. Another open problem is to find alternative associative
operations on cyclic words to generate classes of languages of cyclic
words. Of interest is also the investigation of the language of primitive cyclic
words and its relation to the set of primitive words.
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