P Systems with 2D Picture Grammars

Abstract

In formal language theory of two-dimensions, 2D picture grammars are powerful tools to generate picture languages. In this work, we incorporate the idea of membrane systems (also called P systems) into 2D picture grammars, thus introducing a new kind of picture language generating devices, named P systems with 2D picture grammars. Inspired by the structure and functioning of living cells, such a system has a hierarchical membrane structure, symbol array objects and evolution rules of 2D picture grammars. In each region delimited by the membrane structure, array objects can evolve in a parallel manner according to evolution rules present in the region, like the way biochemical objects evolve in living cells or organisms. The computational result of P system with 2D picture grammars is the set of pictures (rectangular arrays) present in a specific output membrane when the system halts. We obtain several comparison results, which show that with the membrane structure, the generating power of Siromoney matrix grammar, 2D context-free grammar and basic puzzle grammar can be enlarged.