Computing with Membranes and Picture Arrays

Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages

Algebraic Properties of Parikh Matrices of Words under an Extension of Thue Morphism

The Parikh matrix of a word $w$ over an alphabet $\{a_1, \cdots , a_k \}$ with an ordering $a_1 < a_2 < \cdots a_k,$ gives the number of occurrences of each factor of the word $a_1 \cdots a_k$ as a (scattered) subword of the word $w.$ Two words $u,v$ are said to be $M-$equivalent, if the Parikh matrices of $u$ and $v$ are the same. On the other hand properties of image words under different morphisms have been studied in the context of subwords and Parikh matrices. Here an extension to three letters, introduced by S$\acute{e}\acute{e}$bold (2003), of the well-known Thue morphism on two letters, is considered and properties of Parikh matrices of morphic images of words are investigated. The significance of the contribution is that various classes of binary words are obtained whose images are $M-$equivalent under this extended morphism