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EN
We consider the external variant of non-isometric d-dimensional contextual array grammars with regular control together with local selectors allowing for controlling how d-dimensional arrays are evolving by adjoining rectangular (d-1)-dimensional arrays. In the 1-dimensional case, the computational power of these non-isometric contextual array grammars with regular control and local selectors equals the computational power of isometric contextual array grammars with regular control. The string images of the languages of 1-dimensional arrays generated by these contextual array grammars exactly yield the linear languages. In the more-dimensional case, non-isometric d-dimensional contextual array grammars with regular control and local selectors can simulate the computations of (d - 1)-dimensional array grammars or Turing machines. Hence, for example, the emptiness problem for non-isometric d-dimensional contextual array grammars with regular control and local selectors for d > 1 is undecidable. We also compare the computational power of all variants of non-isometric d-dimensional contextual array grammars that we introduce to each other.
EN
It is known that the Common Algorithmic Problem (CAP) has the nice property that several other NP-complete problems can be reduced to it in linear time. The decision version of this problemis known to be efficiently solved by a family of recognizer P systems with activemembranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes without polarizations and present a uniform solution to CAP in the minimally parallel mode.
3
Content available remote A new class of analytic functions based on Ruscheweyh derivative
EN
In this paper we introduce a new class [formula/wzór] consisting of analytic functions with negative coeffcients and investigate various properties and characterization of the class. The results include coeffcient estimates, distortion theorem, closure theorems and integral operators for the class [formula/wzór]. Also radii of close-to-convexity, starlikeness and convexity are determined.
4
Content available remote Array P Systems and t-Communication
EN
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.
5
Content available remote Array Grammars with Contextual Operations
EN
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.
6
Content available remote Tissue-like P Systems with Active Membranes for Picture Generation
EN
We propose a variant of tissue-like P systems with symport rules and active membranes that generates two-dimensional picture languages. The method is unconventional in that, instead of using the membranes as regions for computation/writing, it uses them to hold elements of pictures. Thus, the picture itself, and actually the whole supporting rectangular grid, is composed of membranes, each one containing (among other symbols) a letter of the picture's alphabet. The method is illustrated by its application to the generation of local and recognizable picture languages.
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