Recognizable iso-triangular picture languages

Abstract

In modern civilization, the art of tiling has become a Prerogative pattern.  Tiling patterns have been used to decorate and cover floors and walls.  Motivated by the problem of tiling, H. Wang introduced a tile in 1961, called by his name, Wang tile and in which the edges are coloured.  A finite set of Wang tiles admits a valid tiling of the plane if copies of tiles can be arranged one by one without rotation or reflection to fill the plane so that gluable tiles which have the same colour.  Wang tiling patterns motivate Kalyani et. al to introduce an iso-triangular labelled Wang tiles.  A finite automaton is one of the machines that scan the pictures and recognizes the pictures.  In this paper, we define iso-triangular Wang automaton and iso-triangular Wang P system.  It is showed that an iso-triangular Wang automaton stimulates the computational power of the P system.  The iso-triangular Wang P system recognizes the iso-triangular pictures.  The computational complexity of iso-triangular Wang automaton and iso-triangular Wang P system is examined with the computational powers of iso-triangular Wang system, iso-triangular tiling system and hexagonal tiling system.