P Systems for Array Generation and Application to Kolam Patterns

K. G. Subramanian¹*, R. Saravanan² and T. Robinson³

¹School of Mathematical Sciences, University Sains Malaysia, 11800 Penang, Malaysia
²Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai 600073, India
³Department of Mathematics, Madras Christian College, Chennai 600059, India
*E-mail address: kgs@usm.my

(Received November 3, 2006; Accepted September 5, 2007)

Keywords: Kolam Patterns, Array Language, P-system

Abstract. In the area of membrane computing, a new computability model, now called P system was introduced by PAUN (2002) inspired from the cell structure and its functioning. One area of P systems deals with string objects and rewriting rules. Recently, array P systems with array objects and array rewriting rules were introduced. Here we introduce a new class of array P systems called sequential/parallel rectangular array P systems generating pictures of rectangular arrays. These P systems have rectangular arrays as objects in the membranes and rules in the membranes are either context-free or regular with sequential horizontal rewriting or right-linear rules with vertical rewriting in parallel as in the two-dimensional (2D) matrix grammars (SIROMONEY et al., 1972). These P systems have more generative power and accordingly, they can generate kolam patterns that cannot be handled by 2D matrix grammars.