Shuffle on array languages generated by array grammars

Motivated by the studies done by G. Siromoney et al. (1973) and Alexan- dru Mateescu et al. (1998) we examine the language theoretic results related to shuf- fle on trajectories by making use of Siromoney array grammars such as (R : R)AG, (R : C F )AG, (C F : R)AG, (C F : C F )AG, (C S : R)AG, (C S : C S)AG and (C F : C S)AG which are more powerful than the Siromoney matrix grammars (1972) and are used to make digital pictures

SHUFFLE ON ARRAY LANGUAGES GENERATED BY ARRAY GRAMMARS

Abstract. Motivated by the studies done by G

A Bio-inspired Model of Picture Array Generating P System with Restricted Insertion Rules

In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating $P$ system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array $P$ system

Variants Of Array-Rewriting P Systems For Generating Picture Arrays

Bidang pengkomputeran membran dimulakan sekitar tahun 2000, berinspirasikan struktur dan fungsi sel-sel hidup. Model teori pengkomputeran membran ini dipanggil sistem P dan variannya dan penggunaan model ini dalam pelbagai masalah telah disiasat secara intensif sejak itu. Sistem P tatasusunan menghubungkan tatabahasa tatasusunan bahasa formal dengan sistem P. Dalam teori bahasa formal, salah satu kajian utama adalah terhadap keupayaan tatabahasa untuk menjana bahasa, yang disebut sebagai keupayaan generatif, yang bergantung kepada jenis-jenis peraturan yang digunakan. Kami menyiasat keupayaan generatif sistem P tatasusunan dengan memperkenalkan dalam peraturan sistem ciri-ciri benar, tatabahasa dengan penulisan semula selari dan kaedah mengumpul peraturan. Di sini dengan mengaitkan simbol benar dalam kaedah sistem P tatasusunan, kami memperkenalkan varian baru, yang dinamakan sebagai sistem P tatasusunan dengan ciri-ciri benar. Kami membuktikan bahawa jumlah membran yang digunakan dalam pembinaan itu dapat dikurangkan berbanding sistem P tatasusunan. Kami menggabungkan penulisan semula selari dalam sistem P rentetan di dalam sistem P tatasusuan, dengan itu memperkenalkan satu lagi varian baru dalam sistem P tatasusunan dan dinamakan sebagai sistem P tatasusunan selari. Inspired by the structure and functioning of the living cells, the field of membrane computing was initiated around the year 2000. Since then the theoretical model introduced in this area, called P system has been intensively investigated for properties and applications. One such P system known as array-rewriting P systems provides a link between two dimensional formal language theory and membrane computing. In formal language theory, one of the main studies is on the language generating capability of the grammars, referred to as the generative capacity, which depends on the types of rules. Also a standard technique to increase the generative capacity is to endow the rules with additional features. Here the array-rewriting P system is investigated by endowing the grammatical rules of the system with three such features, namely, permitting symbols, parallel rewriting and grouping of rules. Thus this thesis introduces and develops three such variants of the array-rewriting P system and brings out their advantages

Contextual Array Grammars with Matrix and Regular Control

International audienceWe investigate the computational power of d-dimensional contextual array grammars with matrix control and regular control languages. For $$d\ge 2$$, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. Yet in the 1-dimensional case, for a one-letter alphabet, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages coincides with the family of regular 1-dimensional array languages, whereas for alphabets with more than one letter, we obtain the array images of the linear languages

Contextual Array Grammars with Matrix and Regular Control

International audienceWe investigate the computational power of d-dimensional contextual array grammars with matrix control and regular control languages. For $$d\ge 2$$, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. Yet in the 1-dimensional case, for a one-letter alphabet, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages coincides with the family of regular 1-dimensional array languages, whereas for alphabets with more than one letter, we obtain the array images of the linear languages

PARALLEL CONTEXTUAL ARRAY GRAMMARS WITH TRAJECTORIES

A simple and effective syntactic method of description of picture patterns of rectangular arrays of symbols is proposed. The method is based on contextual grammars of Marcus(1969) guided by trajectories in the generation process.The resulting grammar is called Parallel contextual array grammar with contexts shuffled on trajectories. This grammar is capable of describing pictorial patterns that cannot be handled by certain other contextual array grammars introduced in the literature. 1

Representations Of Recursively Enumerable Array Languages By d-Dimensional Contextual Array Grammars

. The main result proved in this paper shows that the natural embedding of any 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 we conjecture that a similar result is true for arbitrary dimensions. Moreover, we show that for obtaining such a result, in the selectors of the contextual array productions only the ability to distinguish between blank and non-blank positions is necessary. Keywords: Array languages, contextual grammars, shape 1 Introduction With motivations arising from descriptive linguistics, contextual grammars were introduced in [11] for the string case. The contextual string productions are pairs (s; c), where s is a string and called the selector and c is a pair of strings, c = (u; v); over the alphabet under consideration and called the context. Starting from an axiom, iteratively contexts are added as it is..