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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.

Representations of Recursively Enumerable Array Languages by Contextual Array Grammars

Fernau H., Freund R., Holzer M.

Fundamenta Informaticae

2005

Vol. 64, nr 1-4

159-170

The main result proved in this paper shows that the natural embedding of any recursively enumerable one-dimensional array language in the two-dimensional space can be characterized by the projection of a two-dimensional array language generated by a contextual array grammar working in the t-mode and with norm one. Moreover, we show that any recursively enumerable one-dimensional array language can even be characterized by the projection of a two-dimensional array language generated by a contextual array grammar working in the t-mode where in the selectors of the contextual array productions only the ability to distinguish between blank and non-blank positions is necessary; in that case, the norm of the two-dimensional contextual array grammar working in the t-mode cannot be bounded.