On Derivation Languages of Flat Splicing Systems.

In this work, we associate the idea of derivation languages with at splicing systems and compare the languages generated as derivation languages (Szilard and Control languages) with the family of languages in Chomsky hierarchy. We show that there exist regular languages which cannot be generated as a Szilard language by any labeled flat splicing system. But some context-sensitive languages can be generated as a Szilard language by alphabetic labeled flat splicing systems. Also, any regular, context-free and recursively enumerable language can be represented as a homomorphic image of the Szilard language generated by the labeled flat splicing systems of type (1, 2); (2, 3) and (4, 3) respectively. We also introduce the idea of Control languages for labeled finite flat splicing systems and show that any regular and context-free language can be generated as a Control language by these systems of type (1, 2) and (2,*) respectively. At the end we show that any recursively enumerable language can be generated as a Control language of labeled flat splicing systems of type (4, 3) when {\lambda}-labeled rules are allowed.