scholarly journals The formal derivative operator and multifactorial numbers

2019 ◽  
Vol 53 (2) ◽  
pp. 125-137
Author(s):  
Juan Triana ◽  
Rodrigo De Castro
Keyword(s):  
Derivative Operator ◽  
Context Free Grammar ◽  
Context Free ◽  
Context Free Grammars

In this paper some properties, examples and counterexamples about the formal derivative operator defined with respect to context-free grammars are presented. In addition, we show a connection between the context-free grammar G = { a → abr; b → br+1 } and multifactorial numbers. Some identities involving multifactorial numbers will be obtained by grammatical methods.

scholarly journals Static Watson-Crick Context-Free Grammars

2019 ◽  
Vol 15 (10) ◽  
pp. 65 ◽  
Author(s):  
Wan Heng Fong ◽  
Aqilahfarhana Abdul Rahman ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Dna Computing ◽  
Biological Properties ◽  
Dna Molecules ◽  
Context Free Grammar ◽  
Double Stranded Dna ◽  
New Variant ◽  
Sticker System ◽  
Relationship Of ◽  
Context Free ◽  
Context Free Grammars

Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use the feature of Watson-Crick complementarity in DNA computing. Previously, the grammar counterpart of the Watson-Crick automata have been introduced, known as Watson-Crick grammars which are classified into three classes: Watson-Crick regular grammars, Watson-Crick linear grammars and Watson-Crick context-free grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick context-free grammar, which is a grammar counterpart of sticker systems that generates the double-stranded strings and uses rule as in context-free grammar, is introduced. The static Watson-Crick context-free grammar differs from a dynamic Watson-Crick context-free grammar in generating double-stranded strings, as well as for regular and linear grammars. The main result of the paper is to determine the generative powers of static Watson-Crick context-free grammars. Besides, the relationship of the families of languages generated by Chomsky grammars, sticker systems and Watson-Crick grammars are presented in terms of their hierarchy.

A REGULARITY CONDITION FOR CONTEXT-FREE GRAMMARS

2008 ◽  
Vol 19 (04) ◽  
pp. 845-857
Author(s):  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Regularity Condition ◽  
Complexity Measure ◽  
Context Free Grammar ◽  
Context Free ◽  
Context Free Grammars

We define a complexity measure on context-free grammars called end. Roughly speaking, for a context-free grammar G, endG(n) measures the distance of variables from the ends of sentential forms along the derivations of words in L(G) of length n. We prove in a constructive way the regularity of L(G)wheneverendG(n)is constant. Yet, we improve on this by showing that ifL(G)is nonregular thenendG(n) = Ω∞( log n). We establish the optimality of such bound. Finally, we show that, in case of unambiguous context-free grammars, the end lower bound for generating nonregular languages turns out to be linear.

scholarly journals Context-Free Grammars with Graph Controlled Tables

1975 ◽  
Vol 4 (43) ◽  
Author(s):  
Grzegorz Rozenberg ◽  
Arto Salomaa
Keyword(s):  
Context Free Grammar ◽  
Context Sensitive ◽  
Context Free ◽  
Context Free Grammars

It is shown that every context-sensitive language can be generated by a context-free grammar with graph control over sets of productions. This can be done in two different ways, corresponding to unconditional transfer programmed grammars and programmed grammars with empty failure fields. Also some results concerning ordinary programmed grammars are established.

Grammar-based transformations: attack and defence

2014 ◽  
Vol 22 (2) ◽  
pp. 141-154
Author(s):  
Dusan Repel ◽  
Ingo Stengel
Keyword(s):  
Theoretical Investigation ◽  
Frequency Analysis ◽  
Design Methodology ◽  
Empirical Investigation ◽  
Development Environment ◽  
Context Free Grammar ◽  
Content Type ◽  
Context Free ◽  
Context Free Grammars

Purpose – This research aims to propose an attack that de-obfuscates codes by exploiting the properties of context-free grammars since it is important to understand the strength of obfuscation provided by context-free grammar-based obfuscators. In addition, the possibility of automatically generated transformations is explored. Design/methodology/approach – As part of our empirical investigation, a development environment for obfuscating transformations is built. The tool is used to simulate a context-free obfuscator and to devise ways of reversing such transformations. Furthermore, a theoretical investigation of subset grammars and subset languages is carried out. Findings – It is concluded that context-free grammar-based obfuscators provide limited levels of protection. Nevertheless, their application is appropriate when combined with other obfuscating techniques. Research limitations/implications – The algorithms behave as expected on a limited number of test samples. Further work is required to increase their practicality and to establish their average reliability. Originality/value – This research shows how a frequency analysis attack can threaten the security of code scrambled by context-free grammar-based obfuscators.

scholarly journals Description Of Context Free Grammars In Json Format For Parser Generators

2020 ◽  
Vol 23 (6) ◽  
pp. 1301-1323
Author(s):  
Oleg Konstantinovich Osipov
Keyword(s):  
Data Format ◽  
Context Free Grammar ◽  
Parser Generation ◽  
Context Free ◽  
Parser Generator ◽  
Context Free Grammars

Analysis of various presentations for context free grammars provided with parser generators. A new description format of context free grammars is proposed. Given a representation of context free grammar in JSON format. The concept of a new parser generator based on JSON data format of describing context free grammars is presented. Described a parser generation scheme based on that concept.

scholarly journals Equivalent Transformations and Regularization in Context-Free Grammars

2015 ◽  
Vol 14 (4) ◽  
pp. 29-44 ◽  
Author(s):  
Ludmila Fedorchenko ◽  
Sergey Baranov
Keyword(s):  
Formal Language ◽  
Formal Grammar ◽  
Context Free Grammar ◽  
Oriented Graphs ◽  
Right Hand ◽  
Memory Size ◽  
Algol 68 ◽  
Context Free ◽  
Context Free Grammars

Abstract Regularization of translational context-free grammar via equivalent transformations is a mandatory step in developing a reliable processor of a formal language defined by this grammar. In the 1970-ies, the multi-component oriented graphs with basic equivalent transformations were proposed to represent a formal grammar of ALGOL-68 in a compiler for IBM/360 compatibles. This paper describes a method of grammar regularization with the help of an algorithm of eliminating the left/right-hand side recursion of nonterminals which ultimately converts a context-free grammar into a regular one. The algorithm is based on special equivalent transformations of the grammar syntactic graph: elimination of recursions and insertion of iterations. When implemented in the system SynGT, it has demonstrated over 25% reduction of the memory size required to store the respective intermediate control tables, compared to the algorithm used in Flex/Bison parsers.

PARALLEL RECOGNITION OF HIGH DIMENSIONAL IMAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 285-291 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI
Keyword(s):  
Time Complexity ◽  
Random Access ◽  
Space Complexity ◽  
Recognition Problem ◽  
High Dimensional ◽  
Context Free Grammar ◽  
Random Access Machine ◽  
Parallel Random Access Machine ◽  
Context Free ◽  
Context Free Grammars

We investigate the complexity of the recognition of images generated by a class of context-free image grammars. We show that the sequential time complexity of the recognition of an n × n image as generated by a context-free grammar is O(nM(n)), where M(n) is the time to multiply two boolean n × n matrices. The space complexity of this recognition is O(n3). Using a parallel random access machine (i.e. PRAM), the recognition can be done in O( log 2(n)) time with n7 processors or in O(n log 2(n)) time with n6 processors. We also introduce high dimensional context-free grammars and prove that their recognition problem is polylogarithmic.

INSTANCE-SPECIFIC SOLUTIONS FOR ACCELERATING THE CKY PARSING OF LARGE CONTEXT-FREE GRAMMARS

2004 ◽  
Vol 15 (02) ◽  
pp. 403-415 ◽  
Author(s):  
JACIR L. BORDIM ◽  
OSCAR H. IBARRA ◽  
YASUAKI ITO ◽  
KOJI NAKANO
Keyword(s):  
Verilog Hdl ◽  
Context Free Grammar ◽  
Large Context ◽  
Speed Up ◽  
Design Software ◽  
Context Free ◽  
Context Free Grammars

The main contribution of this paper is an FPGA-based implementation of an instance-specific hardware which accelerates the CKY (Cocke-Kasami- Younger) parsing of context-free grammars. Given a context-free grammar G and a string x, the CKY parsing determines whether G derives x. We developed a hardware generator that creates a Verilog HDL source to perform the CKY parsing for any fixed context-free grammar G. The generated source is embedded in an FPGA using the design software provided by the FPGA vendor. The results show that our instance-specific hardware solution attains an astonishing speed-up factor of up to 3,700 over traditional software solutions.

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 Tree Valence Controlled Grammars

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Salbiah Ashaari ◽  
SHERZOD TURAEV ◽  
Abdurahim Okhunov
Keyword(s):  
Structural Properties ◽  
Context Free Grammar ◽  
The Past ◽  
New Variant ◽  
Main Production ◽  
Number Of Publications ◽  
Regular Sets ◽  
Context Free ◽  
Ordinary Context ◽  
Context Free Grammars

Beyond a shadow of a doubt, the studying of context-free grammars with restricted derivationtrees known as tree controlled grammars have achieved plentiful remarkable results within formallanguage theory as demonstrated in a number of publications on this subject for the past forty five years.In principle, these grammars generate their languages as an ordinary context-free grammar except theirderivation trees need to be satisfied by certain prescribed conditions. Our paper is a continuing of studyingof this kind of grammars, where we introduce a new variant of tree controlled grammar called a treevalence controlled grammar, which replaces regular sets with valences where every main production withcertain integer value will be derived into sub-productions with the value of combination of zero and one orzero and minus represented in matrices form with the permutations of each matrix row yield a zero value(at every level of tree derivation, the summation of valence value is zero). We also investigate thegenerative capacity and structural properties of these grammars.

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