Parallel Contextual Array Insertion Deletion Grammars, Pure 2D Context-Free Grammars and Associated P Systems

Abstract

Syntactic models constitute one of the main areas of mathematical studies on picture array generation. A number of 2D grammar models have been proposed with motivation from a variety of applications. Parallel Contextual Array Insertion Deletion Grammar (PCAIDG) and Pure 2D Context-Free Grammar (P2DCFG) are two such 2D grammars. In the case of P2DCFG, two new variants are studied with interesting properties. In this paper we show that PCAIDG has higher generative power than the generative powers of two variants of P2DCFG. Further, P systems associated with the grammars PCAIDG, P2DCFG and their variants are considered in the literature. In this paper, we show that the generative power of Parallel Contextual Array Insertion Deletion P System (PCAIDPS) is greater than the generative power of the P system associated with a variant of P2DCFG.