Abstract families of matrices and picture languages
TL;DR: A linguistic model to generate matrices (arrays of terminals) is presented and immediate application is shown in picture processing by generating a wide class of interesting pictures.
About: This article is published in Computer Graphics and Image Processing.The article was published on 1972-11-01. It has received 167 citations till now.
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TL;DR: Investigations into Drosophila Wing Development - Results from a Lindenmayer Model and the Theoretical Basis of the Transplantation Experiment.
Abstract: Investigations into Drosophila Wing Development - Results from a Lindenmayer Model.- Fibonacci Words - A Survey.- Planar Map Generation by Parallel Binary Fission/Fusion Grammars.- Modular Trellises.- A New Proof for the DOL Sequence Equivalence Problem and its Implications.- On Compound Lindenmayer Systems.- Graph Grammars with Application Conditions.- The ETOL Hierarchy is in the OI Hierarchy.- Polyhedral Cell Shapes.- On Cyclically Overlap-Free Words in Binary Alphabets.- The Theoretical Basis of the Transplantation Experiment.- Fixed and Stationary ?-Words and ?-Languages.- DOL Schemes and Recurrent Words.- Stochastic OL Systems and Formal Power Series.- Complexity of L-Systems.- Compartmental Hybrid State Production-Diffusion Systems with Application to Prestalk-Prespore Pattern Regulation in Cellular Slime Molds.- Hierarchical Aspects of Plant Development.- Rule Trees Represent Derivations in Edge Replacement Systems.- Languages Defined by Indian Parallel Systems.- L Systems and NLOG-Reductions.- The Parikh-Boundedness of ETOL Languages of Finite Index.- Computer Networks with Compact Routing Tables.- Unconventional Leaves.- A Uniform Model for the Growth of Biological Organisms: Cooperating Sequential Processes.- Graph Technology Applied to a Software Project.- Some Systems for Map Generation.- A Programming Language for Lindenmayer Systems.- A Note on Significance of Cellular Interaction in L-System.- EOL Grammars and Search Trees.- Variation in Inflorescence Structure in Cotoneaster Franchetti.- Partial Path Groups and Parallel Graph Contractions.- When L was Young.- Equivalence Problems for Regular Sets of Word Morphisms.- Parentheses Grammars and Lindenmayer Grammars.- Array Languages and Lindenmayer Systems - A Survey.- Symmetric Distributed Termination.- Development, Growth and Time.- On the Set of all Subgraphs of the Graphs in a Boundary NLC Graph Language.- Graph-Controlled Systems - An Extension of OL Systems.
191 citations
TL;DR: Generative models of picture languages with array rewriting rules are presented and each letter of the alphabet of different sizes can be generated by a context-free array grammar.
Abstract: Generative models of picture languages with array rewriting rules are presented. The rewriting rules are regular, context-free or context-sensitive with arrays of terminals in the place of strings of terminals. Derivations are restricted by the condition for row and column catenation. The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. A distinct hierarchy is shown to exist between the different classes introduced. The models are closed under reflection (about base and rightmost vertical), halfturn, quarter-turn, transpose, and conjugation. Further closure properties such as union, product, star and homomorphism are examined. The models can be applied to generate several interesting patterns of kolam and to describe the repetitive patterns of two-dimensional crystallography. Each letter of the alphabet of different sizes can be generated by a context-free array grammar.
139 citations
21 Jun 2010
TL;DR: In this paper, a library of common spreadsheet usage patterns are automatically extracted and transformed into class diagrams, which can then be used by software engineers to understand, refine, or re-implement the spreadsheet's functionality.
Abstract: The use of spreadsheets to capture information is widespread in industry. Spreadsheets can thus be a wealthy source of domain information. We propose to automatically extract this information and transform it into class diagrams. The resulting class diagram can be used by software engineers to understand, refine, or re-implement the spreadsheet's functionality. To enable the transformation into class diagrams we create a library of common spreadsheet usage patterns. These patterns are localized in the spreadsheet using a two- dimensional parsing algorithm. The resulting parse tree is transformed and enriched with information from the library. We evaluate our approach on the spreadsheets from the Euses Spreadsheet Corpus by comparing a subset of the generated class diagrams with reference class diagrams created manually.
93 citations
TL;DR: It is proved that the P systems with context-free rules are computationally universal, able to generate all computable array languages.
Abstract: We consider array languages (sets of pictures consisting of symbols placed in the lattice points of the 2D grid) and the possibility to handle them with P systems. After proving binary normal forms for array matrix grammars (which, even in the case when no appearance checking is used, are known to generate the array languages of arbitrary array grammars), we prove that the P systems with context-free rules (with three membranes and no control on the communication or the use of rules) are computationally universal, able to generate all computable array languages. Some open problems are also formulated.
84 citations
TL;DR: Kolam designs of South Indian folk art are treated as examples of two-dimensional picture languages, and many of the complicated kolain patterns are seen to be generable by context-free array grammars.
70 citations
References
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40,330 citations
"Abstract families of matrices and p..." refers background in this paper
...Narasimhan has proposed and implemented schemes for the recognition of handprinted letters os the English alphabet [9] and for the generation of poster pictures [10]....
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TL;DR: The relative merits of performing local operations on ~ digitized picture in parallel or sequentially are discussed and some applications of the connected component and distance functions are presented.
Abstract: The relative merits of performing local operations on ~ digitized picture in parallel or sequentially are discussed. Sequential local operations are described which l~bel the connected components of a given subset of the picture and compute u \"distance\" from every picture element to the subset. In terms of the \"distance\" function, ~ \"skeleton\" subset is defined which, in a certain sense, minimally determines the original subset. Some applications of the connected component and distance functions are also presented.
1,707 citations
"Abstract families of matrices and p..." refers background in this paper
...For practical purposes it is desirable to work wie_h operat ions on digi t ized pictures which can be def ined in terms of func t ions having considerably fewer arguments [11]....
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Book•
01 Jan 1969TL;DR: The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.
Abstract: From the Preface (See Front Matter for full Preface)
The study of formal languages constitutes an important subarea of computer science. This area sprang to life around 1956 when Noam Chomsky gave a mathematical model of a grammar in connection with his study of natural languages. Shortly afterwards, the concept of a grammar was found to be of great importance to the programmer when the syntax of the programming language ALGOL was defined by a context-free grammar. This development led naturally to syntax-directed compiling and the concept of a compiler compiler. Since then a considerable flurry of activity has taken place, the results of which have related formal languages and automata theory to such an extent that it is impossible to treat the areas separately. By now, no serious study of computer science would be complete without a knowledge of the techniques and results from language and automata theory.
This book presents the theory of formal languages as a coherent theory and makes explicit its relationship to automata. The book begins with an explanation of the notion of a finite description of a language. The fundamental descriptive device--the grammar--is explained, as well as its three major subclasses--regular, context-free, and context-sensitive grammars. The context-free grammars are treated in detail, and such topics as normal forms, derivation trees, and ambiguity are covered. Four types of automata equivalent to the four types of grammars are described. These automata are the finite automaton, the pushdown automaton, the linear bounded automaton, and the Turing machine. The Turing machine is covered in detail, and unsolvability of the halting problem shown. The book concludes with certain advanced topics in language theory--closure properties, computational complexity, deterministic pushdown automata, LR(k) grammars, stack automata, and decidability.
1,595 citations
TL;DR: A formal picture description scheme to be used as the basis for picture processing systems is presented and a series of examples illustrate the capability and limitations of the description scheme.
Abstract: A formal picture description scheme to be used as the basis for picture processing systems is presented. The scheme is applicable to a large class of pictures including, but not restricted to, those containing line-like elements. The paper first presents a general linguistic model for picture processing in which the analysis and generation of pictures are defined as the derivation and execution, respectively, of descriptions. A particular realization of the descriptive component of the model including some of its formal properties is then given; a picture class is described in terms of its underlying graph structures by a grammar generating strings in a picture description language. A series of examples illustrate the capability and limitations of the description scheme. Some applications of implemented systems to the analysis and generation of pictures are discussed.
257 citations
"Abstract families of matrices and p..." refers background in this paper
...Thus those pictures of PDL [13] described by these operations can be descr ibed in terms of matrices using generalized superimposition....
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...T h e p r imi t ive i t se l f can be d e s c r i b e d us ing m e t h o d s alr e a d y p u b l i s h e d [8,13] 9 S + EXAMPLE 2....
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...Shaw [13] has abs t racted primitives into vectors with a tail and a head and by def ining cer ta in basic operations such as +, • , , - , and a generative grammar, descr ibes wide classes of pictures....
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...Shaw [13] has pointed out that some of the limitations of his picture description languages (PDL) are that they cannot describe simple operations such as rotation, magnification, etc....
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...Also superimposition helps us to reintell~ret for matrices the basic operations in Shaw's picture description languages [13]....
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