Analysis of the non-context-free component of formal languages

1976 ◽  
pp. 230-236 ◽  
Author(s):  
Michal P. Chytil
Keyword(s):  
Formal Languages ◽  
Context Free

Growth of Groups

2017 ◽  
Author(s):  
Eric Freden
Keyword(s):  
Word Length ◽  
Polynomial Growth ◽  
Formal Languages ◽  
Research Projects ◽  
Growth Theorem ◽  
Generating Set ◽  
Growth Series ◽  
Growth Of Groups ◽  
Counting Methods ◽  
Context Free

This chapter considers the growth of a group. It begins with the case of a group with a given finite generating set, in which the ball B(1, r) of radius r centered at the identity 1 is the set of group elements whose word length is less than or equal to r. Given a group that is fixed and some r greater than or equal to 0, the chapter invokes Gromov's polynomial growth theorem to determine how many group elements are in B(1, r) and how many group elements are in S(1, r). It also explores the use of simple counting methods to compute several growth series before concluding with an overview of cone types, formal languages and context-free grammars, and the DSV method used to compute the growth of grammar productions. The discussion includes exercises and research projects.

Formal languages defined by the underlying structure of their words

1988 ◽  
Vol 53 (4) ◽  
pp. 1009-1026 ◽  
Author(s):  
J. P. Ressayre
Keyword(s):  
Natural Extension ◽  
Formal Languages ◽  
Finite Union ◽  
Underlying Structure ◽  
Theoretic Approach ◽  
Local Language ◽  
Infinite Words ◽  
Context Sensitive ◽  
Context Free ◽  
Local Languages

Abstracti) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages, ii) We define local languages, a class of languages between free local and context-sensitive languages. Each local language L has a natural extension L∞ to infinite words, and we prove a series of “pumping lemmas”, analogs for each local language L of the “uvxyz theorem” of context free languages: they relate the existence of large words in L or L∞ to the existence of infinite “progressions” of words included in L, and they imply the decidability of various questions about L or L∞. iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals.We hope that these results are useful for a model-theoretic approach to the theory of formal languages.

scholarly journals Consensus Game Acceptors and Iterated Transductions

2018 ◽  
Vol 29 (02) ◽  
pp. 165-185
Author(s):  
Dietmar Berwanger ◽  
Marie van den Bogaard
Keyword(s):  
Imperfect Information ◽  
Formal Languages ◽  
Finite Graph ◽  
Context Sensitive ◽  
Model Based ◽  
Context Free

We study a game for recognising formal languages, in which two players with imperfect information should coordinate on a common decision, given private input words correlated by a finite graph. The players have a common objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input. We show that the acceptor model based on consensus games characterises context-sensitive languages. Further, we describe the expressiveness of these games in terms of iterated synchronous transductions and identify a subclass that characterises context-free languages.

UNSOLVABILITY LEVELS OF OPERATION PROBLEMS FOR SUBCLASSES OF CONTEXT-FREE LANGUAGES

2005 ◽  
Vol 16 (03) ◽  
pp. 423-440 ◽  
Author(s):  
HENNING BORDIHN ◽  
MARKUS HOLZER ◽  
MARTIN KUTRIB
Keyword(s):  
Open Problem ◽  
Formal Languages ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Power Operation ◽  
The Given ◽  
Context Free ◽  
Free Language

We investigate the operation problem for linear and deterministic context-free languages: Fix an operation on formal languages. Given linear (deterministic, respectively) context-free languages, is the application of this operation to the given languages still a linear (deterministic, respectively) context-free language? Besides the classical operations, for which the linear and deterministic context-free languages are not closed, we also consider the recently introduced root and power operation. We show non-semi-decidability, to be more precise, we show completeness for the second level of the arithmetic hierarchy for all of the aforementioned operations, except for the power operation, if the underlying alphabet contains at least two letters. The result for the power operation solves an open problem stated in Theoret. Comput. Sci.314 (2004) 445–449.

The word problem of ℤ n is a multiple context-free language

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Meng-Che Ho
Keyword(s):  
Word Problem ◽  
Regular Language ◽  
Formal Languages ◽  
Strong Connection ◽  
Context Free Language ◽  
Multiple Context ◽  
Context Free ◽  
Free Language

Abstract The word problem of a group {G=\langle\Sigma\rangle} can be defined as the set of formal words in {\Sigma^{*}} that represent the identity in G. When viewed as formal languages, this gives a strong connection between classes of groups and classes of formal languages. For example, Anīsīmov showed that a group is finite if and only if its word problem is a regular language, and Muller and Schupp showed that a group is virtually-free if and only if its word problem is a context-free language. Recently, Salvati showed that the word problem of {\mathbb{Z}^{2}} is a multiple context-free language, giving the first example of a natural word problem that is multiple context-free, but not context-free. We generalize Salvati’s result to show that the word problem of {\mathbb{Z}^{n}} is a multiple context-free language for any n.

ON THE LEFTMOST DERVIATION IN MATRIX GRAMMARS

1999 ◽  
Vol 10 (01) ◽  
pp. 61-79 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
HENNING FERNAU ◽  
GHEORGHE PĂUN
Keyword(s):  
Systematic Study ◽  
Regular Language ◽  
Formal Languages ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Leftmost Derivation ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

Matrix grammars are one of the classical topics of formal languages, more specifically, regulated rewriting. Although this type of control on the work of context-free grammars is one of the earliest, matrix grammars still raise interesting questions (not to speak about old open problems in this area). One such class of problems concerns the leftmost derivation (in grammars without appearance checking). The main point of this paper is the systematic study of all possibilities of defining leftmost derivation in matrix grammars. Twelve types of such a restriction are defined, only four of which being discussed in literature. For seven of them, we find a proof of a characterization of recursively enumerable languages (by matrix grammars with arbitrary context-free rules but without appearance checking). Other three cases characterize the recursively enumerable languages modulo a morphism and an intersection with a regular language. In this way, we solve nearly all problems listed as open on page 67 of the monograph [7], which can be seen as the main contribution of this paper. Moreover, we find a characterization of the recursively enumerable languages for matrix grammars with the leftmost restriction defined on classes of a given partition of the nonterminal alphabet.

scholarly journals Definition of Natural Languages Using Context-free Grammer: In Context of Dari Language

2019 ◽  
Vol 4 (2) ◽  
pp. 167-170
Author(s):  
Mahmood Asgharzada
Keyword(s):  
Natural Language ◽  
Formal Language ◽  
Formal Languages ◽  
Natural Languages ◽  
Computer Scientists ◽  
The Common ◽  
To Come ◽  
Definition Of ◽  
Context Free ◽  
Free Language

Formal definition of a natural language lets computers understand it; the languages have challenging complexity to come under representation of any formal language. Modeling assumptions, using formal languages, we can approximate the languages; and better approximation we do, more complexities of formal languages are resolved. Objective is to study current researches and possibilities to model Dari as a context-free language. Researchers have worked for more than 6 decades on definition of syntax of natural languages using context-free grammer. It is crucial that computer scientists to be able to thoroughly understand about which category of formal languages the natural language exist in in. In overall, our skill to decide the grammar type of natural languages performs a significant role in our capability to parse it. This review article concludes that discussed issue of the context-freeness of a certain language is regularly reliant on upon the level of complexity of the language. The common of languages investigated in this regard are languages of European family and Indo-Aryan languages liker Dari, Arabic and Pashto have not been adequately fortunate to be devoted thorough researches in this regard.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

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