Infinite arrays and infinite computations

AbstractA complete metric topology is introduced on the set of all finite and infinite arrays and the topological properties of the space are studied. In this complete metric topology, infinite arrays are the limits of increasing sequences of finite arrays. The notion of successful infinite derivations in Generalized Context-free Kolam Array Grammars, yielding infinite arrays, is a subclass of Generalized context-free kolam array grammars. For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated by it are related through the notion of adherence

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

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

Pure 2D picture grammars and languages

A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids

Adjunct hexagonal array token Petri nets and hexagonal picture languages

Adjunct Hexagonal Array Token Petri Net Structures (AHPN) are re- cently introduced hexagonal picture generating devices which extended the Hexag- onal Array Token Petri Net Structures . In this paper we consider AHPN model along with a control feature called inhibitor arcs and compare it with some ex- pressive hexagonal picture generating and recognizing models with respect to the generating power

Generating similar images using bag context picture grammars

A Dissertation submitted to the Faculty of Science in partial fulfilment of the requirements for the degree of Master of Science University of the Witwatersrand, Johannesburg, February 2018Formal language theory was born in the middle of the 20th century as a tool for modeling and investigating syntax of natural languages. It was developed in connection with the handling of programming languages. Bag context grammars are a fairly new grammar class where bag context tree grammars have been defined. Bag context is used to regulate rewriting in tree grammars. In this dissertation we use bag context to regulate rewriting in picture grammars and thus to generate similar pictures. This work is exploratory work since bag context picture grammars have not been defined. We use examples to show how bag context picture grammars can be used to generate pictures. In this work bag context picture grammars are defined and used to generate similar pictures. Pictures generated by random context picture grammars and three of their sub-classes are selected and bag context picture grammars are used to generate the same pictures to those selected. A lemma is defined that is used to convert the class of random context picture grammars and three of their sub-classes into equivalent bag context picture grammars. For each grammar selected, an equivalent bag context picture grammar is created and used to generate several pictures that are similar to each other. Similarity is defined by noting small differences that are seen in pictures that belong to the same gallery. In this work we generate similar pictures with bag context picture grammars and thus make the discovery that bag context gives a certain level of control in terms of rules applied in a grammar.XL201

Methods for Structural Pattern Recognition: Complexity and Applications

Katedra kybernetik

Computing with Membranes and Picture Arrays

Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages