Partial commutation on some classes of 2D picture languages

Abstract

The concept of partial commutation and traces on strings has been recently extended to rectangular picture arrays and languages, motivated by the two-dimensional patterns which appear in studies concerning parallel computing and image analysis. The closure property of Siromoney matrix languages (SML) under partial commutation is already studied. In this paper, we consider partial commutation on a generalization of SML languages and Siromoney array languages (SAG) and establish some interesting results. Also, we examine the partial commutativity applied on some higher classes of 2D picture languages generated by Regional tile rewriting grammars and Prusa grammars. We extend partial commutation concept to hexagonal pictures also.