Iso-array rewriting P systems with context-free iso-array rules

A new computing model called P system is a highly distributed and parallel theoretical model, which is proposed in the area of membrane computing. Ceterchi et al. initially proposed array rewriting P systems by extending the notion of string rewriting P systems to arrays (2003). A theoretical model for picture generation using context-free iso-array grammar rules and puzzle iso-array grammar rules are introduced by Kalyani et al. (2004, 2006). Also iso-array rewriting P systems for iso-picture languages have been studied by Annadurai et al. (2008). In this paper we consider the context-free iso-array rules and context-free puzzle iso-array rules in iso-array rewriting P systems and examine the generative powers of these P systems

Array Tissue-like P Systems

Array grammars have been studied in the framework of Membrane Comput- ing by using rewriting rules from transition P systems. In this paper we present a new approach to dealing with array grammars by using tissue-like P systems and present an application to the segmentation of images in two dimensional computer graphics.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420

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

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

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

Finite difference methods fengshui: alignment through a mathematics of arrays

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.Peer ReviewedPostprint (author's final draft

Performance of VIDEBAS in an operational environment

VIDEBAS is a relational database management system in which a database consists of two parts, namely a “real-only” and an “update” part. The first part remains unmodified until the next reorganization and exploits redundancy to achieve fast access to data. A prototype of VIDEBAS has been built. In this paper a performance comparison between this relational system and a DBTG-system (UDS) is made. The used external memory and the number of page accesses to retrieve and update tuples is estimated. Although it is commonly assumed that in an operational environment relational systems are slower than network systems the opposite appears. On the other hand UDS needs less external memory

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality