On the finiteness of picture languages of synchronous deterministic chain code picture systems

Chain Code Picture Systems are LINDENMAYER systems over a special alphabet. The strings generated are interpreted as pictures. This leads to Chain Code Picture Languages. In this paper, synchronous deterministic Chain Code Picture Systems (sDOL systems) are studied with respect to the finiteness of their picture languages. First, a hierarchy of abstractions is developed, in which the interpretation of a string as a picture passes through a multilevel process. Second, on the basis of this hierarchy, an algorithm is designed which decides the finiteness or infiniteness of any sDOL system in polynomial time

Perfectly quilted rectangular snake tilings

AbstractWe introduce a particular form of snake tilings to define picture languages, and relate the obtained family to the recognizable picture languages (as defined by Wang tiles). The correspondence for substitution tilings is even closer, and hence is applicable to the Hilbert curve

Picture words with invisible lines

AbstractA picture word is a word over the alphabet {r, r̄, u, ū, rb, r̄b, ub, ūb}. With any picture word, we associate a picture as follows: the reading of each letter of the word induces a unit move; the letters r and rb (r̄ and r̄b, u and ub, ū and ūb) stand for a right (left, up, down) move; for each letter from {r, r̄, u, ū}, we move by drawing a unit line; for the other letters, we move with “pen-up”. We present a rewriting system S which generates exactly all the picture words describing a given picture

Representation does matter

In Machine Learning the main problem is that of learning a ‘description’ of a class (possibly an infinite set) from a finite num- ber of positive and negative training examples. For real world problems, however, one must distinguish between the actual instance of the class to be learned and the numeric or symbolic encoding of the instances of the same class. The question here is whether different encodings (or representations) of the instances of a real-world class can actually affect the performance of the learning algorithm. In artificial neural networks (ANNs), for example, it is required that the classes are always encoded as vectors over some field (usually the set of reals). In this paper it is argued that the representation of the class instances plays a very important role in machine learning since it has bearing on two very important issues — the structural completeness of the training set and also the inductive bias of the learning algorithm.peer-reviewe

Two-Dimensional Picture Grammar Models.

A new theoretical model of grammatical picture generation called extended 2D context-free picture grammar (E2DCFPG) generating rectangular picture arrays of symbols is introduced. This model which allows variables in the grammar and uses the squeezing mechanism of forming the picture language over terminal symbols, is an extension of the pure 2D context-free picture grammar (P2DCFPG) [13]. The extended picture grammar model E2DCFPG is shown to have more picture generative power than the P2DCFPG and certain other existing 2D models. Certain closure and other properties of this new model are also examine

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

Language generating alphabetic flat splicing P systems

An operation on strings, called at splicing was introduced, inspired by a splicing operation on circular strings considered in the study of modelling of the recombinant behaviour of DNA molecules. A simple kind of at splicing, called alphabetic at splicing, allows insertion of a word with a specified start symbol and/or a specified end symbol, between two pre-determined symbols in a given word. In this work, we consider a P system with only alphabetic at splicing rules as the evolution rules and strings of symbols as objects in its regions. We examine the language generative power of the resulting alphabetic at splicing P systems (AFS P systems, for short). In particular, we show that AFS P systems with two membranes are more powerful in generative power than AFS P systems with a single membrane. We also construct AFS P systems with at most three membranes to generate languages that do not belong to certain other language classes and show an application to generation of chain code pictures