scholarly journals Undecidable problems concerning densities of languages

2005 ◽  
Vol DMTCS Proceedings vol. AF,... (Proceedings) ◽  
Author(s):  
Jakub Kozik
Keyword(s):  
Relative Density ◽  
Context Free Grammar ◽  
International Audience ◽  
Context Free ◽  
Context Free Grammars

International audience In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no algorithm which, given two unambiguous context free grammars on input, decides whether the language defined by the first grammar has a relative density in the language defined by the second one. Our techniques can be extended to show that this problem is undecidable even for languages given by grammars from $LL(k)$ (for sufficiently large fixed $k ∈ \mathbb{N} )$.

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 On a property of probabilistic context-free grammars

1983 ◽  
Vol 6 (2) ◽  
pp. 403-407 ◽  
Author(s):  
R. Chaudhuri ◽  
A. N. V. Rao
Keyword(s):  
Population Density ◽  
Relative Density ◽  
Terminal Symbol ◽  
Context Free Language ◽  
Context Free ◽  
Probabilistic Context ◽  
Free Language ◽  
Context Free Grammars ◽  
Probabilistic Context Free Grammars

It is proved that for a probabilistic context-free languageL(G), the population density of a character (terminal symbol) is equal to its relative density in the words of a sampleSfromL(G)whenever the production probabilities of the grammarGare estimated by the relative frequencies of the corresponding productions in the sample.

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 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 Coefficients of algebraic functions: formulae and asymptotics

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Cyril Banderier ◽  
Michael Drmota
Keyword(s):  
Critical Exponents ◽  
Entire Functions ◽  
Limit Laws ◽  
Context Free Grammar ◽  
Algebraic Functions ◽  
Strongly Connected ◽  
International Audience ◽  
Planar Maps ◽  
Dyadic Numbers ◽  
Context Free

International audience This paper studies the coefficients of algebraic functions. First, we recall the too-little-known fact that these coefficients $f_n$ have a closed form. Then, we study their asymptotics, known to be of the type $f_n \sim C A^n n^{\alpha}$. When the function is a power series associated to a context-free grammar, we solve a folklore conjecture: the appearing critical exponents $\alpha$ can not be $^1/_3$ or $^{-5}/_2$, they in fact belong to a subset of dyadic numbers. We extend what Philippe Flajolet called the Drmota-Lalley-Woods theorem (which is assuring $\alpha=^{-3}/_2$ as soon as a "dependency graph" associated to the algebraic system defining the function is strongly connected): We fully characterize the possible critical exponents in the non-strongly connected case. As a corollary, it shows that certain lattice paths and planar maps can not be generated by a context-free grammar (i.e., their generating function is not $\mathbb{N}-algebraic). We end by discussing some extensions of this work (limit laws, systems involving non-polynomial entire functions, algorithmic aspects). Cet article a pour héros les coefficients des fonctions algébriques. Après avoir rappelé le fait trop peu connu que ces coefficients $f_n$ admettent toujours une forme close, nous étudions leur asymptotique $f_n \sim C A^n n^{\alpha}$. Lorsque la fonction algébrique est la série génératrice d'une grammaire non-contextuelle, nous résolvons une vieille conjecture du folklore : les exposants critiques $\alpha$ ne peuvent pas être $^1/_3$ ou $^{-5}/_2$ et sont en fait restreints à un sous-ensemble des nombres dyadiques. Nous étendons ce que Philippe Flajolet appelait le théorème de Drmota-Lalley-Woods (qui affirme que $\alpha=^{-3}/_2$ dès lors qu'un "graphe de dépendance" associé au système algébrique est fortement connexe) : nous caractérisons complètement les exposants critiques dans le cas non fortement connexe. Un corolaire immédiat est que certaines marches et cartes planaires ne peuvent pas être engendrées par une grammaire non-contextuelle non ambigüe (i. e., leur série génératrice n'est pas $\mathbb{N}-algébrique). Nous terminons par la discussion de diverses extensions de nos résultats (lois limites, systèmes d'équations de degré infini, aspects algorithmiques).

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.

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