Derivation languages and descriptional complexity measures of restricted flat splicing systems

Abstract

In this paper, we associate the idea of derivation languages with a restricted variant of flat splicing systems where at each step splicing is done with an element from the initial set of words present in the system. We call these flat splicing systems as restricted flat splicing systems. We show that the families of Szilard languages of labeled restricted flat finite splicing systems of type (m,n) and REG, CF and CS are incomparable. Also, any non-empty regular, non-empty context-free and recursively enumerable language can be obtained as homomorphic image of the Szilard language of the labeled restricted flat finite splicing systems of type (1,2),(2,2) and (5,2) respectively. We also introduce the idea of control languages for restricted labeled flat finite splicing systems and show that any non-empty regular and context-free language can be obtained as a control language of labeled restricted flat finite splicing systems of type (1,2) and (2,2) respectively. At the end, we show that any recursively enumerable language can be obtained as a control language of labeled restricted flat finite splicing systems of type (5,2) when λ-labeled rules are allowed.