On bonded sequential and parallel insertion systems

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 127-151
Author(s):  
Markus Holzer ◽  
Bianca Truthe ◽  
Ahmad Firdaus Yosman
Keyword(s):  
Parallel System ◽  
Lindenmayer Systems ◽  
Generative Capacity ◽  
Closure Properties ◽  
Time Step ◽  
Chomsky Hierarchy ◽  
Sequential System ◽  
New Variant

We introduce a new variant of insertion systems, namely bonded insertion systems. In such systems, words are not only formed by usual letters but also by bonds between letters. Words which can be inserted, have “free” bonds at their ends which control at which positions in a word they can be inserted (namely only there, where the bonds “fit”). Two kinds of bonded insertion systems are defined in this paper: so-called bonded sequential insertion systems and bonded parallel insertion systems. In a sequential system, there is only one word inserted at a time. In a parallel system, there is a word inserted at every possible position in parallel in one time step. We investigate the generative capacity of those two kinds and relate the families of generated languages to some families of the Chomsky hierarchy and to families of languages generated by Lindenmayer systems. Additionally, we investigate some closure properties.

Representation of the Variable Chain Mechanisms With Sequential Movement

2006 ◽  
Author(s):  
Hsing-Hui Huang
Keyword(s):  
Topological Structure ◽  
Parallel System ◽  
Degree Of Freedom ◽  
Composite Function ◽  
Sequential System ◽  
Sequential Movement ◽  
Parallel Movement ◽  
One Step ◽  
System Movement

A mechanism that encounters a certain change in the number of links or degree of freedom during operation will also result the variation of the topological structure in every stage. Since the mechanisms with variable chain in different stages during operation have different topologies, but the applications of this kind of mechanisms are very extensively. And this also result the complications of representation of the topology thoroughly. Mechanisms with variable chain now always been represented by graph according to the topology of each stage, but hardly represent by using a formula. We would like to propose an approach to develop the function for representing the mechanism with variable chain that focus on the sequential movement, and help the representation of the operation not only by the graph but also by the function. According to the operation of the mechanisms with variable chain, the movement of the mechanisms can be classified into parallel system movement and sequential system movement. Parallel movement mechanisms are the mechanisms operate more than one links in the same time when giving an input; and when we give an input that can operate just only one link and effect and transfer the movement of the next one step by step, we can call this kind of mechanisms as sequential mechanisms. In this work we apply composite function for represent the movement of each stage, and also verified the representation by applying it on the existed examples.

A COMPARISON OF THE DESCRIPTIONAL COMPLEXITY OF CLASSES OF LIMITED LINDENMAYER SYSTEMS: PART I

2012 ◽  
Vol 23 (01) ◽  
pp. 99-114
Author(s):  
RONNY HARBICH ◽  
BIANCA TRUTHE
Keyword(s):  
The Other ◽  
Lindenmayer Systems ◽  
Generative Capacity ◽  
Descriptional Complexity

We investigate the descriptional complexity of limited Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. In this part, we confine ourselves to propagating limited Lindenmayer systems. 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.

Chomsky Hierarchy Control on Isotonic Array P Systems

2016 ◽  
Vol 30 (02) ◽  
pp. 1650004 ◽  
Author(s):  
Williams Sureshkumar ◽  
Raghavan Rama
Keyword(s):  
P Systems ◽  
Generative Capacity ◽  
Chomsky Hierarchy

In this paper, we propose a new regulated evolution in P systems with isotonic arrays and isotonic array rules. The regulated language will be a language of Chomsky hierarchy. This model generates interesting pictures for a given regulated language. The generative capacity is explored.

CONTEXT-FREE GRAMMARS WITH LINKED NONTERMINALS

2007 ◽  
Vol 18 (06) ◽  
pp. 1271-1282 ◽  
Author(s):  
ANDREAS KLEIN ◽  
MARTIN KUTRIB
Keyword(s):  
Generative Capacity ◽  
Closure Properties ◽  
Rewriting Systems ◽  
Rewriting System ◽  
The Family ◽  
Infinite Degree ◽  
New Type ◽  
Equivalent Systems ◽  
Context Free ◽  
Context Free Grammars

We introduce a new type of finite copying parallel rewriting system, i. e., grammars with linked nonterminals, which extend the generative capacity of context-free grammars. They can be thought of as having sentential forms where some instances of a nonterminal may be linked. The context-free-like productions replace a nonterminal together with its connected instances. New links are only established between symbols of the derived subforms. A natural limitation is to bound the degree of synchronous rewriting. We present an infinite degree hierarchy of separated language families with the property that degree one characterizes the family of regular and degree two the family of context-free languages. Furthermore, the hierarchy is a refinement of the known hierarchy of finite copying rewriting systems. Several closure properties known from equivalent systems are summarized.

Watson–Crick Jumping Finite Automata: Combination, Comparison and Closure

2021 ◽  
Author(s):  
U K Mishra ◽  
K Mahalingam ◽  
R Rama
Keyword(s):  
Finite Automata ◽  
Closure Properties ◽  
Computing Power ◽  
New Model ◽  
Model Of Computation ◽  
Chomsky Hierarchy ◽  
Restricted Version ◽  
State 1

Abstract A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

scholarly journals MACROS, Iterated Substitution and Lindenmayer AFLs

1973 ◽  
Vol 2 (18) ◽  
Author(s):  
Arto Salomaa
Keyword(s):  
Lindenmayer Systems ◽  
Closure Properties ◽  
Open Problems ◽  
Weak Closure ◽  
The Family ◽  
Context Free

The notion of a K-iteration grammar, where K is a family of languages, provides a uniform framework for discussing the various language families obtained by context-free Lindenmayer systems. It is shown that the family of languages generated by K-iteration grammars possesses strong closure properties under the assumption that K itself has certain weak closure properties. Along these lines, the notion of a hyper-AFL is introduced and some open problems are posed.

ON THE DESCRIPTIONAL COMPLEXITY OF LINDENMAYER SYSTEMS

2004 ◽  
Vol 15 (04) ◽  
pp. 663-672 ◽  
Author(s):  
JÜRGEN DASSOW
Keyword(s):  
Lindenmayer Systems ◽  
Generative Capacity ◽  
Descriptional Complexity ◽  
Special Cases

We define the number of productions and the number of symbols as measures of descriptional complexity for tabled interactionless Lindenmayer systems and their special cases. We investigate the decrease of the descriptional complexities if we go from a family to another one which has a larger generative capacity.

FINITE IMAGES GENERATED BY GL-SYSTEMS

1989 ◽  
Vol 03 (03n04) ◽  
pp. 459-467 ◽  
Author(s):  
A. SAOUDI ◽  
K. RANGARAJAN ◽  
V. R. DARE
Keyword(s):  
Parallel Systems ◽  
Algebraic Characterization ◽  
Lindenmayer Systems ◽  
Closure Properties ◽  
New Device ◽  
Pumping Lemma

In this paper, we introduce a new device called GL-systems (i.e. Grammar-Lindenmayer systems) for generating finite images. GL-systems are sequential/parallel systems in which the horizontal rules form a Chomskian grammar and the vertical rules form a DTOL system. We obtain hierarchical results of various types of GL-systems. We study some properties like, closure properties, combinatorial results, pumping lemma and decidability results. An algebraic characterization for GL-systems (with variation) is presented.

Semiconditional Contextual Grammars

1985 ◽  
Vol 8 (2) ◽  
pp. 151-161
Author(s):  
Gheorghe Păun
Keyword(s):  
Generative Capacity ◽  
Chomsky Hierarchy

One defines a class of contextual grammars “intermediate” between the conditional contextual grammars and the contextual grammars with bounded choice (the addition of each context depends on a prefix and a suffix of the current string which belong to a given pair of languages associated with this context). The paper investigates the generative capacity of these grammars compared to other contextual language families and with families in Chomsky hierarchy.

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