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.

GENERATIVE CAPACITY OF SUBREGULARLY TREE CONTROLLED GRAMMARS

2010 ◽  
Vol 21 (05) ◽  
pp. 723-740 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
RALF STIEBE ◽  
BIANCA TRUTHE
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Derivation Tree ◽  
Generative Capacity ◽  
The Family ◽  
Context Free ◽  
Context Free Grammars

Tree controlled grammars are context-free grammars where the associated language only contains those terminal words which have a derivation where the word of any level of the corresponding derivation tree belongs to a given regular language. We present some results on the power of such grammars where we restrict the regular languages to some known subclasses of the family of regular languages.

scholarly journals Closure properties of static Watson-Crick linear and context-free grammars

2020 ◽  
Author(s):  
Aqilahfarhana Abdul Rahman ◽  
Wan Heng Fong ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Closure Properties ◽  
Context Free ◽  
Context Free Grammars

scholarly journals EOL and ETOL Systems with Control Devices

1974 ◽  
Vol 3 (37) ◽  
Author(s):  
Mogens Nielsen
Keyword(s):  
Vector Control ◽  
Generative Capacity ◽  
Regular Control ◽  
Control Devices ◽  
Context Free ◽  
Context Free Grammars

The effects of 1) regular control, 2) appearance checking, and 3) minimal table interpretation on extended (partial table) OL systems with respect to the generative capacity are studied. It is proved that the effect of 3) is strictly stronger that the effects of 1) and 2), and equal to the effect of the combination of l) and 2). This implies among other things that appearance checking increases the generative capacity of the systems with regular control - the corresponding problem for ordinary grammars being still open. Finally, the notions of matrix and vector control are introduced and some results on the effects of these mechanisms are proved. These results turn out to be very much different from the corresponding well-known results for context free grammars-differences, of course, due to the different natures of CF-grammars and EOL-systems.

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.

scholarly journals Generative Power and Closure Properties of Watson-Crick Grammars

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nurul Liyana Mohamad Zulkufli ◽  
Sherzod Turaev ◽  
Mohd Izzuddin Mohd Tamrin ◽  
Azeddine Messikh
Keyword(s):  
Proper Subset ◽  
Computational Power ◽  
Closure Properties ◽  
Generative Power ◽  
Context Sensitive ◽  
Closure Operations ◽  
The Family ◽  
Grammar Rules ◽  
Almost All ◽  
Context Free

We defineWK linear grammars, as an extension of WK regular grammars with linear grammar rules, andWK context-free grammars, thus investigating their computational power and closure properties. We show that WK linear grammars can generate some context-sensitive languages. Moreover, we demonstrate that the family of WK regular languages is the proper subset of the family of WK linear languages, but it is not comparable with the family of linear languages. We also establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations.

On Pure Context-Free Languages and Left Szilard Languages

1991 ◽  
Vol 15 (1) ◽  
pp. 86-89
Author(s):  
Erkki Mäkinen
Keyword(s):  
Generative Capacity ◽  
Negative Results ◽  
Context Free ◽  
Context Free Grammars

It is shown that left Szilard languages of context-free grammars are pure context-free languages. This is one of the few exceptions among the numerous negative results concerning the generative capacity of pure languages. Moreover, we characterize pure context-free languages and left Szilard languages of pure context-free grammars as certain homomorphic images.

scholarly journals The generative capacity of block-synchronized context-free grammars

2005 ◽  
Vol 337 (1-3) ◽  
pp. 119-133 ◽  
Author(s):  
I. McQuillan
Keyword(s):  
Generative Capacity ◽  
Context Free ◽  
Context Free Grammars

scholarly journals Computational Power of Static Watson-Crick Context-free Grammars

2019 ◽  
Vol 1 (2) ◽  
pp. 82-85
Author(s):  
Wan Heng Fong ◽  
Aqilahfarhana Abdul Rahman ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Computer Model ◽  
Dna Computing ◽  
Research Finding ◽  
Biological Properties ◽  
Computational Power ◽  
Context Free Grammar ◽  
The Family ◽  
Sticker System ◽  
Context Free ◽  
Context Free Grammars

Sticker system is a computer model which is coded with single and double-stranded molecules of DNA; meanwhile, Watson-Crick automata is the automata counterpart of the sticker system representing the biological properties of DNA. Both are the modelings of DNA molecules in DNA computing which use the feature of Watson-Crick complementarity. Formerly, Watson-Crick grammars which are classified into three classes have been introduced [1]. In this research, a grammar counterpart of sticker systems that uses the rule as in context-free grammar is introduced, known as a static Watson-Crick context-free grammar. The research finding on the computational power of these grammar shows that the family of context-free languages is strictly included in the family of static Watson-Crick context-free languages; the          static Watson-Crick context-free grammars can generate non context-free languages; the family of Watson-Crick context-free languages is included in the family of static Watson-Crick context-free languages which are presented in terms of their hierarchy.

scholarly journals CONTEXT-FREE REWRITING SYSTEMS AND WORD-HYPERBOLIC STRUCTURES WITH UNIQUENESS

2012 ◽  
Vol 22 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ALAN J. CAIN ◽  
VICTOR MALTCEV
Keyword(s):  
Hyperbolic Structure ◽  
Hyperbolic Structures ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Context Free

This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan and Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid).

Jumping Grammars

2015 ◽  
Vol 26 (06) ◽  
pp. 709-731 ◽  
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Finite Index ◽  
Open Problems ◽  
Generative Power ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x → y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x. The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars. A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

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