Parallel Contextual Array Insertion Deletion P System S. James Immanuel 1(B ) , D.G. Thomas 1 , Robinson Thamburaj 1 , and Atulya K. Nagar 2 1 Department of Mathematics, Madras Christian College, Tambaram, Chennai 600059, India james imch@yahoo.co.in , dgthomasmcc@yahoo.com , robin.mcc@gmail.com 2 Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, UK nagara@hope.ac.uk Abstract. We introduce a new P system model called as parallel con- textual array insertion deletion P system, based on the modified row and column contextual rules of parallel contextual array grammar. We can generate a family of two-dimensional picture languages using this P sys- tem. We discuss some properties of this P system and find its generating power by comparing this new family of languages with that of certain other well known families of two-dimensional picture languages. Keywords: P system · Rectangular array · Parallel contextual array 1 Introduction One of the extensions of string language theory is two-dimensional languages. There has been a continued interest in adapting the techniques of formal string language theory for developing methods to study the problem of picture genera- tion and description, where pictures are considered as connected, digitized finite arrays in the two-dimensional plane. The literature on array grammars and array acceptors has steadily grown over the past several years. Rosenfeld [16, 17] has investigated isometric array genration, pointing out the need for array rewriting rules for picture languages. In an array grammar, the idea is to have rewriting rules that allow replacement of a subarray of a picture with another subarray, thus generalizing the Chomskian string grammars to arrays. Siromoney et al. [18] proposed a simple generative model, called two- dimensional matrix grammar, to describe digital pictures viewed as rectangular arrays of terminals. Motivated by the need to generate picture languages that cannot be generated by two-dimensional matrix grammars, Siromoney et al. [19] introduced array models, generalizing the notion of rewriting rules in which the catenation of strings is extended to row and column catenation of arrays. While the study of formal language theory has its origins in Chomskian gram- mars, another class of grammars, called contextual grammars was introduced by c  Springer International Publishing AG 2017 V.E. Brimkov and R.P. Barneva (Eds.): IWCIA 2017, LNCS 10256, pp. 170–183, 2017. DOI: 10.1007/978-3-319-59108-7 14