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

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

Solving 2D-pattern matching with networks of picture processors

We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts simultaneously all subpictures of the same size from the input picture and sends them to the second subnetwork. The second subnetwork checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterwards, we present a solution based on networks containing both evolutionary and hiding processors running in O(n+m+kl+k) computational (processing and communication) steps, where the input picture and the pattern are of size (n,m) and (k,l), respectively

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

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Predictive uncertainty in auditory sequence processing

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A Picture Array Generating Model Based on Flat Splicing Operation

The bio-inspired operations of linear and circular splicing respectively on linear and circular strings of symbols have been extensively investigated by many researchers for their theoretical properties. Recently, another kind of splicing of two words, referred to as flat splicing on strings, has been considered. We here extend this operation to flat splicing on picture arrays, thus defining a new model of picture generation, which we call as array flat splicing system (AF S) and obtain some results on the generative power of AF S in comparison with certain well-known picture array defining model