On the Descriptional Complexity of Limited Propagating Lindenmayer Systems

We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when the generative capacity is increased. For incomparable families, we give languages that can be described more efficiently in either of these families than in the other.Comment: In Proceedings DCFS 2010, arXiv:1008.127

On the Number of Membranes in Unary P Systems

We consider P systems with a linear membrane structure working on objects over a unary alphabet using sets of rules resembling homomorphisms. Such a restricted variant of P systems allows for a unique minimal representation of the generated unary language and in that way for an effective solution of the equivalence problem. Moreover, we examine the descriptional complexity of unary P systems with respect to the number of membranes

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

Tree façades : generative modelling with an axial branch rewriting system

The methods and algorithms of generative modelling can be improved when representing organic structures by the study of computational models of natural processes and their application to architectural design. In this paper, we present a study of the generation of branching structures and their application to the development of façade support systems. We investigate two types of branching structures, a recursive bifurcation model and an axial tree based L-system for the generation of façades. The aim of the paper is to capture not only the form but also the underlying principles of biomimicry found in branching. This is then tested, by their application to develop experimental façade support systems. The developed algorithms implement parametric variations for façade generation based on natural tree-like branching. The benefits of such a model are: ease of structural optimization, variations of support and digital fabrication of façade components

P and dP Automata: A Survey

This is a quick survey of basic notions and results related to P automata (P systems with symport/antiport rules working in the accepting mode), with some emphasis on the recently introduced dP automata (a distributed version of the standard P automata), ending with some open problems and research topics which we find of interest in this area.Junta de Andalucía P08 – TIC 0420

New variants of insertion and deletion systems in formal languages

In formal language theory, the operations of insertion and deletion are generalizations of the operations of concatenation and left/right quotients. The insertion operation interpolates one word in an arbitrary place within the other while the deletion operation extracts the word from an arbitrary position of another word. Previously, insertion and deletion have been applied to model the recombinance of DNA and RNA molecules in DNA computing, where contexts were used to mimic the site of enzymatic activity. However, in this research, new systems are introduced by taking motivation from the atomic behaviour of chemical compounds during chemical bonding, in which the concept of a balanced arrangement is required for a successful bonding. Besides that, the relation between insertion and deletion systems and group theory are also shown. Here, insertion and deletion systems are constructed with bonds and also interactions; hence new variants of insertion and deletion systems are introduced. The first is bonded systems, which are introduced by defining systems with restrictions that work on the bonding alphabet. The other variant is systems with interactions, which are introduced by utilizing the binary operations of certain groups as the systems’ interactions. From this research, the generative power and closure properties of the newly introduced bonded systems are determined, and a language hierarchy is constructed. In addition, group generating insertion systems are introduced and illustrated using Cayley graphs. Therefore, this research introduced new variants of insertion and deletion systems that contribute to the advancement of DNA computing and also showcased their application in group theory

An infinite hierarchy induced by depth synchronization

AbstractDepth-synchronization measures the number of parallel derivation steps in a synchronized context-free (SCF) grammar. When not bounded by a constant the depth-synchronization measure of an SCF grammar is at least logarithmic and at most linear with respect to the word length. Languages with linear depth-synchronization measure and languages with a depth-synchronization measure in between logarithmic and linear are proven to exist. This gives rise to a strict infinite hierarchy within the family of SCF (and ET0L) languages

Fractal Based on Noise for Batik Coloring using Normal Gaussian Method

Noise is an un-expected signal which exists naturally at any system. In the study of fractal batik coloring, noise as a spot is generated as the basis of batik motive coloring. Even distribution of noise spots will produce art-works which involve elements of culture and technology. The development of batik motives and colors could be harmonized with the development of technology, such as the use of fractal method in order to create the new motives of batik. Fractal is a geometric form which can be separated into pieces, where each part is the repeated small version. The coloring of batik was based on the generating noise using Gaussian method. Noise on fractal batik was spots which were generated randomly on the surface of fractal batik, meanwhile Gaussian method was a noise model which followed normal distribution standard with zero average and standard deviation 1.The generating noise as coloring basis of fractal batik patterns, which was formed in the previous study, showed the distant error of noise between 9.1 pixels and 13.7 pixels. This was because the distribution of noise on the fractal batik patterns was carried out randomly using Gaussian method for every process of fractal rewriting system

On the number of components in cooperating distributed grammar systems

AbstractIt is proved that the number of components in context-free cooperating distributed (CD) grammar systems can be reduced to 3 when they are working in the so-called sf-mode of derivation, which is the cooperation protocol which has been considered first for CD grammar systems. In this derivation mode, a component continues the derivation until and unless there is a nonterminal in the sentential form which cannot be rewritten according to that component. Moreover, it is shown that CD grammar systems in sf-mode with only one component can generate only the context-free languages but they can generate non-context-free languages if two components are used. The sf-mode of derivation is compared with other well-known cooperation protocols with respect to the hierarchies induced by the number of components