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Picture Languages Generated by Assembling Tiles

Bonizzoni P., Ferretti C., Mary A. R. S., Mauri G.

Fundamenta Informaticae

2011

Vol. 110, nr 1-4

77-93

We propose a new formalism for generating picture languages based on an assembly mechanism of tiles that uses rules having a context and a replacement site. More precisely, a picture language will be generated from a finite set of initial pictures by iteratively applying rewriting rules from a given finite set of rules, called a tiling rule system (TRuS system). We prove that the TRuS systems have a greater generative capacity than the tiling systems of Giammarresi and Restivo. This is due mainly to the use of the notion of replacement site, but we further characterize the difference between these systems by comparing them to Wang systems.

Array P Systems and t-Communication

Subramanian K.G., Ali R.M., Nagar A.K., Margenstern M.

Fundamenta Informaticae

2009

Vol. 91, nr 1

145-159

The two areas of grammar systems and P systems, which have provided interesting computational models in the study of formal string language theory have been in the recent past effectively linked in [4] by incorporating into P systems, a communication mode called t-mode of cooperating distributed grammar systems. On the other hand cooperating array grammar systems [5] and array P systems [1] have been developed in the context of two-dimensional picture description. In this paper, motivated by the study of [4], these two systems are studied by linking them through the t-communication mode, thus bringing out the picture description power of these systems.

Array Grammars with Contextual Operations

Subramanian K.G., Van Do Long, Chandra P.H., Quyen N.D.

Fundamenta Informaticae

2008

Vol. 83, nr 4

411-428

In this paper, we consider a class of two-dimensional array grammars, called parallel contextual array grammars, that extend the contextual operations on strings to arrays in a natural way and generate languages of pictures of rectangular arrays. Several classes of these array grammars and the resulting families of picture languages are considered. Necessary conditions for picture languages to be contained in these classes are obtained and the relations between these families are also established.