Flat splicing context free array grammar systems generating picture arrays

Abstract

In the area of DNA computing, a biologically motivated operation called splicing on linear words as well as circular words was introduced by Head 1987, 1992. Motivated by this operation, the concept of flat splicing on words was introduced by Berstel et al. 2012. This operation was extended by Subramanian et al. 2015a to picture arrays. Based on flat splicing on picture arrays, a new model of picture generation known as flat splicing regular array grammar system FSRAGS was also proposed by Subramanian et al. 2015b. Here we extend this model by considering a well-known two-phase context-free grammar in the components of the grammar system with the components deriving picture arrays in parallel using the rules and with two different components communicating using the array flat splicing operations. We call the resulting model as flat splicing context-free array grammar system FSCFAGS and obtain certain theoretical results on the generative power of FSCFAGS. As an application we construct a FSCFAGS and a corresponding algorithm to generate a certain class of floor design, also called a kolam pattern.