scholarly journals On the Decidability of some Equivalence Problems for D0L-Systems

1973 ◽  
Vol 2 (20) ◽  
Author(s):  
Mogens Nielsen
Keyword(s):  
Open Problem ◽  
Equivalence Problem ◽  
Lindenmayer Systems ◽  
L Systems ◽  
And Control ◽  
Equivalence Problems

One of the questions of the longest open standing in the area of Lindenmayer-systems is the decidability of the equivalence problem for deterministic, informationless L-systems (DOL-Systems). This and some related equivalence-problems (equivalence with respect to the set and the sequence of generated words, Parikh-vectors and word-lengths) are investigated. Some of these related problems are shown to be recursively solvable, and the implications of these results on the main open problem mentioned above are discussed. (The paper has been accepted for publication in Information and Control).

A Bioinspired Approach Combining L-Systems and Cellular Automata for Distributed Self-Reconfiguration of UBot Modular Robotic Systems

2016 ◽  
Author(s):  
Dongyang Bie ◽  
Yanhe Zhu ◽  
JiZhuang Fan ◽  
Xiaolu Wang ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Robotic Systems ◽  
Self Organization ◽  
Lindenmayer Systems ◽  
Topological Description ◽  
Biological Principle ◽  
L Systems ◽  
Automatic Planning ◽  
And Control ◽  
Organizing Principles

Self-reconfiguration of Modular Self-Reconfigurable (MSR) robots is a fundamental primitive that can be used as part of higher-lever functionality. The biological principle of self-organizing and growth in both animals and plants is learned to solve the automatic planning of configuration and control methods. A bioinspired approach is proposed for distributed self-reconfiguration. This method aims at utilizing the self-organization and pattern emergence of the MSR robotic system, which is made of large quantity of modules to promote the system to reconfigure in the direction of adapting to environments and tasks. This mechanism is hybrid by combining Lindenmayer systems (L-systems) and Cellular Automata (CA). L-systems are introduced for defining global structure and providing topological description. Cellular Automata (CA) handle motion planning of distributed modules. This method is absolutely distributed and convergent to self-adaptive structures with desired organizing principles. The convergence of proposed method is verified through simulations and experiments on UBot robots.

ON THE NUMBER OF ACTIVE SYMBOLS IN LINDENMAYER SYSTEMS

2011 ◽  
Vol 22 (01) ◽  
pp. 223-235 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
GYÖRGY VASZIL
Keyword(s):  
Lindenmayer Systems ◽  
L System ◽  
L Systems

A symbol a is called active in an L system G if there is a rule a → υ with a ≠ υ in some table of G. By AcX(L) we denote the number of active symbols necessary to generate L by L systems of type X. For two types X and Y of L systems such that the corresponding languages families [Formula: see text] and [Formula: see text] satisfy [Formula: see text], we say that Y is more efficient than X, if there is a sequence of languages [Formula: see text], n ≥ 1, such that AcX(Ln) ≥ n and AcY(Ln) ≤ k for some constant k. In this paper we shall show that the inclusion [Formula: see text] implies that Y is more efficient than X. Analogous results are presented for some modifications of the measure of active symbols.

scholarly journals The Application of Translation Strategies to Cope With Equivalence Problems in Translating Texts

2018 ◽  
Vol 1 (1) ◽  
pp. 1-9
Author(s):  
Dhini Aulia
Keyword(s):  
Equivalence Problem ◽  
Target Language ◽  
Source Text ◽  
Translation Process ◽  
Translation Strategies ◽  
Source Language ◽  
Specific Concept ◽  
Equivalence Problems

Translation is a process to render the meaning from the source text into the target text. A translator, however, will find some problems during translation process. Equivalence is the case which often appears (i.e. culture specific concept, the source-language concept is not lexicalized in the target language, source-language word is semantically complex, etc). To cope with equivalnce problems in translation process, some experts suggest some strategies which can be applied in doing translation. Some strategies are transference, naturalization, cultural equivalent, etc. The strategies which often appears in the example texts in this paper are transference, naturalization, descriptive equivalent, couplet and  through-translation. It is recomended that translator apply the strategies if only there is no equivalence problem in target language. 

Resolution of well-known resistivity equivalences by inclusion of time-domain induced polarization data

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. E47-E54 ◽  
Author(s):  
Line Meldgaard Madsen ◽  
Gianluca Fiandaca ◽  
Anders Vest Christiansen ◽  
Esben Auken
Keyword(s):  
Time Domain ◽  
Equivalence Problem ◽  
Induced Polarization ◽  
Monte Carlo Algorithm ◽  
High Resistivity ◽  
Inversion Method ◽  
Model Parameters ◽  
Clay Layer ◽  
Equivalent Models ◽  
Equivalence Problems

The principle of equivalence is known to cause nonuniqueness in interpretations of direct current (DC) resistivity data. Low- or high-resistivity equivalences arise when a thin geologic layer with a low/high resistivity is embedded in a relative high-/low-resistivity background formation causing strong resistivity-thickness correlations. The equivalences often make it impossible to resolve embedded layers. We found that the equivalence problem could be significantly reduced by combining the DC data with full-decay time-domain induced polarization (IP) measurements. We applied a 1D Markov chain Monte Carlo algorithm to invert synthetic DC data of models with low- and high-resistivity equivalences. By applying this inversion method, it is possible to study the space of equivalent models that have an acceptable fit to the observed data, and to make a full sensitivity analysis of the model parameters. Then, we include a contrast in chargeability into the model, modeled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data in combination. The results show that the addition of IP data largely resolves the DC equivalences. Furthermore, we present a field example in which DC and IP data were measured on a sand formation with an embedded clay layer known from a borehole drilling. Inversion results show that the DC data alone do not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.

On the Decidability of Some Equivalence Problems for L Algebraic Series

1997 ◽  
Vol 07 (03) ◽  
pp. 339-351 ◽  
Author(s):  
Juha Honkala
Keyword(s):  
Equivalence Problem ◽  
Special Cases ◽  
Equivalence Problems

The equivalence problem for Lindenmayerian algebraic series is discussed. While the problem in general is undecidable, decidable special cases of interest are presented.

scholarly journals Complexity of Some Problems Concerning Lindenmayer Systems. (Revised version)

1979 ◽  
Vol 7 (85) ◽  
Author(s):  
Neil D. Jones ◽  
Sven Skyum
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Turing Machines ◽  
Lindenmayer Systems ◽  
L Systems

<p>We determine the computational complexity of membership, emptiness and infiniteness for several types of L systems. The L systems we consider are EDOL, EOL, EDTOL, and ETOL, with and without empty productions. For each problem and each type of system we establish both upper and lower bounds on the time or memory required for solution by Turing machines.</p><p>Revised version (first version 1978 under the title <em>Complexity of Some Problems Concerning: Lindenmayer Systems</em>)</p>

scholarly journals Physarum Polycephalum Syllogistic L-Systems and Judaic Roots of Unconventional Computing

2016 ◽  
Vol 44 (1) ◽  
pp. 181-201 ◽  
Author(s):  
Andrew Schumann
Keyword(s):  
Physarum Polycephalum ◽  
Unconventional Computing ◽  
Lindenmayer Systems ◽  
L Systems

Abstract We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems (L-systems), where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, second, a Talmudic syllogistic by qal wa-homer.

scholarly journals Arterial Branching within the Confines of Fractal L-System Formalism

2001 ◽  
Vol 118 (3) ◽  
pp. 267-276 ◽  
Author(s):  
M. Zamir
Keyword(s):  
Asymmetry Ratio ◽  
Lindenmayer Systems ◽  
Fractal Structures ◽  
Random Choice ◽  
Tree Structures ◽  
L System ◽  
Branching Patterns ◽  
Fractal Characteristics ◽  
L Systems ◽  
The Asymmetry

Parametric Lindenmayer systems (L-systems) are formulated to generate branching tree structures that can incorporate the physiological laws of arterial branching. By construction, the generated trees are de facto fractal structures, and with appropriate choice of parameters, they can be made to exhibit some of the branching patterns of arterial trees, particularly those with a preponderant value of the asymmetry ratio. The question of whether arterial trees in general have these fractal characteristics is examined by comparison of pattern with vasculature from the cardiovascular system. The results suggest that parametric L-systems can be used to produce fractal tree structures but not with the variability in branching parameters observed in arterial trees. These parameters include the asymmetry ratio, the area ratio, branch diameters, and branching angles. The key issue is that the source of variability in these parameters is not known and, hence, it cannot be accurately reproduced in a model. L-systems with a random choice of parameters can be made to mimic some of the observed variability, but the legitimacy of that choice is not clear.

Modeling the architecture of expanding Fraxinus pennsylvanica shoots using L-systems

1994 ◽  
Vol 72 (5) ◽  
pp. 701-714 ◽  
Author(s):  
P. W. Prusinkiewicz ◽  
W. R. Remphrey ◽  
C. G. Davidson ◽  
M. S. Hammel
Keyword(s):  
Computer Graphics ◽  
Computer Animation ◽  
Field Data ◽  
Plant Architecture ◽  
Developmental Model ◽  
Fraxinus Pennsylvanica ◽  
Green Ash ◽  
Lindenmayer Systems ◽  
L System ◽  
L Systems

This paper presents a mathematical model of Fraxinus pennsylvanica (green ash) shoots, which yields realistic computer graphics images of shoot geometry, and makes it possible to visualize shoot expansion using computer animation. The model is based on the mathematical formalism of Lindenmayer systems (L-systems). The paper emphasizes the process of model construction, with the aim of making the methodology applicable to other plant species. The central issue is the identification of field data necessary to build a comprehensive developmental model of plant architecture. Key words: Fraxinus pennsylvanica, plant architecture, shoot expansion, modeling, L-system, computer graphics.

scholarly journals The geometry of fourth-order differential operator

2015 ◽  
Vol 12 (05) ◽  
pp. 1550055
Author(s):  
Rohollah Bakhshandeh-Chamazkoti
Keyword(s):  
Fourth Order ◽  
Differential Operators ◽  
Necessary Conditions ◽  
Equivalence Problem ◽  
Order Differential Operator ◽  
General Fiber ◽  
Gauge Equivalence ◽  
Sufficient And Necessary Conditions ◽  
Fourth Order Differential Operator ◽  
Equivalence Problems

In the present paper, the equivalence problem for fourth-order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are considered. First, the direct equivalence problem and second equivalence problem is to determine the sufficient and necessary conditions on two fourth-order differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.

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