AN EFFICIENT ALGORITHM TO TEST WHETHER A BINARY AND PROLONGEABLE REGULAR LANGUAGE IS GEOMETRICAL

2009 ◽  
Vol 20 (04) ◽  
pp. 763-774 ◽  
Author(s):  
JEAN-MARC CHAMPARNAUD ◽  
JEAN PHILIPPE DUBERNARD ◽  
HADRIEN JEANNE
Keyword(s):  
Discrete Geometry ◽  
Efficient Algorithm ◽  
Regular Language ◽  
Practical Interest ◽  
Regular Languages ◽  
Regular Case ◽  
Deterministic Automaton ◽  
Model Based ◽  
Temporal Validation ◽  
The Family

Our aim is to present an efficient algorithm that checks whether a binary regular language is geometrical or not, based on specific properties of its minimal deterministic automaton. Geometrical languages have been introduced in the framework of off-line temporal validation of real-time softwares. Actually, validation can be achieved through both a model based on regular languages and a model based on discrete geometry. Geometrical languages are intended to develop a link between these two models. The regular case is of practical interest regarding to implementation features, which motivates the design of an efficient geometricity test addressing the family of regular languages.

Bounded Prefix-Suffix Duplication: Language Theoretic and Algorithmic Results

2015 ◽  
Vol 26 (07) ◽  
pp. 933-952 ◽  
Author(s):  
Marius Dumitran ◽  
Javier Gil ◽  
Florin Manea ◽  
Victor Mitrana
Keyword(s):  
Efficient Algorithm ◽  
Regular Language ◽  
Regular Languages ◽  
Sufficient Condition ◽  
Membership Problem

We consider a restricted variant of the prefix-suffix duplication operation, called bounded prefix-suffix duplication. It consists in the iterative duplication of a length-bounded prefix or suffix of a given word. We give a sufficient condition for the closure of a class of languages under bounded prefix-suffix duplication. Consequently, we get that the class of regular languages is closed under bounded prefix-suffix duplication; furthermore, we propose an algorithm which decides whether a regular language is a finite k-prefix-suffix duplication language. An efficient algorithm solving the membership problem for the k-prefix-suffix duplication of a language is also presented. Finally, we define the k-prefix-suffix duplication distance between two words, extend it to languages and show how it can be computed for regular languages.

scholarly journals Decidability of regular language genus computation

2019 ◽  
Vol 29 (9) ◽  
pp. 1428-1443
Author(s):  
Guillaume Bonfante ◽  
Florian L. Deloup
Keyword(s):  
Regular Language ◽  
New Genus ◽  
Regular Languages ◽  
Minimal Size ◽  
Deterministic Automaton ◽  
Letter Alphabet ◽  
New Family ◽  
Generic Class ◽  
Deterministic Automata ◽  
The Difference

AbstractThis article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of |L|gen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size |L|gen can grow at least exponentially in size |L|. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genus-based hierarchies of regular languages and in particular, we show a new family of regular languages on a two-letter alphabet having arbitrary high genus.

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.

A Note on Pf(k) – Parsable Languages

1991 ◽  
Vol 14 (3) ◽  
pp. 283-286
Author(s):  
Tudor Balanescu ◽  
Marian Gheorghe
Keyword(s):  
Homomorphic Image ◽  
Regular Language ◽  
Regular Languages ◽  
Infinite Hierarchy ◽  
The Family ◽  
Pumping Lemma

This paper investigates the class of regular languages which are pf(k) – parsable. It is shown that k induces an infinite hierarchy in the family of regular languages and that every regular language is a homomorphic image of a pf(O) -parsable language. A pumping lemma for pf – parsable languages is also provided.

SOME REMARKS ON THE HAIRPIN COMPLETION

2010 ◽  
Vol 21 (05) ◽  
pp. 859-872 ◽  
Author(s):  
FLORIN MANEA ◽  
VICTOR MITRANA ◽  
TAKASHI YOKOMORI
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Decision Problems ◽  
Strict Sense ◽  
Closure Properties ◽  
New Words ◽  
The Family

We consider several problems regarding the iterated or non-iterated hairpin completion of some subclasses of regular languages. Thus we obtain a characterization of the class of regular languages as the weak-code images of the k-hairpin completion of center-disjoint k-locally testable languages in the strict sense. This result completes two results from [3] and [11]. Then we investigate some decision problems and closure properties of the family of the iterated hairpin completion of singleton languages. Finally, we discuss some algorithms regarding the possibility of computing the values of k such that the non-iterated or iterated k-hairpin completion of a given regular language does not produce new words.

scholarly journals Further steps on the reconstruction of convex polyominoes from orthogonal projections

2021 ◽  
Author(s):  
Paolo Dulio ◽  
Andrea Frosini ◽  
Simone Rinaldi ◽  
Lama Tarsissi ◽  
Laurent Vuillon
Keyword(s):  
Discrete Geometry ◽  
Convex Subset ◽  
Convex Sets ◽  
A Priori ◽  
Orthogonal Projections ◽  
Reconstruction Process ◽  
Combinatorial Properties ◽  
The Family ◽  
Discrete Counterpart ◽  
Interior Part

AbstractA remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321–347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.

A new underwater positioning model based on average sound speed

2021 ◽  
pp. 1-17
Author(s):  
Yixu Liu ◽  
Xiushan Lu ◽  
Shuqiang Xue ◽  
Shengli Wang
Keyword(s):  
Efficient Algorithm ◽  
Sound Speed ◽  
Incident Angle ◽  
Function Model ◽  
Positioning Accuracy ◽  
Correction Model ◽  
Model Based ◽  
Underwater Positioning ◽  
Speed Function ◽  
The Relationship

Abstract The layout of seafloor datum points is the key to constructing the seafloor geodetic datum network, and a reliable underwater positioning model is the prerequisite for achieving precise deployment of the datum points. The traditional average sound speed positioning model is generally adopted in underwater positioning due to its simple and efficient algorithm, but it is sensitive to incident angle related errors, which lead to unreliable positioning results. Based on the relationship between incident angle and sound speed, the sound speed function model considering the incident angle has been established. Results show that the accuracy of positioning is easily affected by errors related to the incident angle; the new average sound speed correction model based on the incident angle proposed in this paper is used to significantly improve the underwater positioning accuracy.

scholarly journals Interaction in quasibinary systems based on TlSbP2Se6 and compounds of the Tl2Se-Sb2Se3 system

2019 ◽  
Vol 85 (3) ◽  
pp. 20-26
Author(s):  
Viktoria Sabov ◽  
Мaria Potorij ◽  
Iwan Kityk ◽  
Mykhailo Filep ◽  
Marian Sabov
Keyword(s):  
Cross Sections ◽  
Near Infrared ◽  
Practical Interest ◽  
Infrared Range ◽  
Thermally Stable ◽  
Quaternary Compound ◽  
Metal Compounds ◽  
Temperature Method ◽  
The Family ◽  
Near Infrared Range

Complex chalcogenides display semiconductor properties. In particular, heavy metal compounds that are formed in the Tl2Se-Sb2Se3 system are good thermoelectric materials. At the same time TlSbP2Se6 compound belongs to the family of hexaseleno-hypodiphosphates, which representatives have a number of interesting properties (optoelectric, non-linear, etc.) in the near infrared range. The combination of these properties in one material causes some scientific and practical interest, therefore our research was aimed to study the nature of the interaction between TlSbP2Se6 and the thermally stable phases of the Tl2Se-Sb2Se3 system in order to find new promising candidate for applications in electronic devices. The alloys were prepared from corresponding binary, ternary compounds and quaternary TlSbP2Se6 by a direct one-temperature method in evacuated quartz ampoules at temperatures above the melting point of the initial and final products. The initial compounds were synthesized by the reaction of their high purity component elements in stoichiometric proportion. According to the results of the research, it was found that cross-sections based on TlSbP2Se6 and the thermally stable compounds of the Tl2Se-Sb2Se3 section are quasibinary: Sb2Se3–TlSbP2Se6 and TlSbSe2–TlSbP2Se6. Tl9SbSe6 – TlSbP2Se6 and Tl2Se - TlSbP2Se6 systems are not quasibinary, instead quasibinary sections Tl2Se-Tl4P2Se6 and Tl9SbSe6-Tl4P2Se6 which crossing their. The phase equilibrium in Sb2Se3 – TlSbP2Se6 and TlSbSe2 – TlSbP2Se6 systems were studied by common differential thermal analysis (DTA), X-ray powder diffraction (XRD) and microstructure analysis. The eutectic interactions are observed in both systems. The invariant points coordinates are: 77 mol.% TlSbP2Se6, 709 K (system Sb2Se3 – TlSbP2Se6) and 45 mol.% TISbSe2, 680 K (system TlSbSe2 – TlSbP2Se6). Significant boundary solid solutions are formed on the basis of the quaternary compound. Their region extends up to 10 mol% in the system Sb2Se3 – TlSbP2Se6 and to about 18 mol.% in the system TlSbSe2 –TlSbP2Se6 at annealing temperature (573 К). Near the Sb2Se3 and TlSbSe2, the solubility limits do not exceed several mol.%.

scholarly journals Konstruowanie tożsamości w warunkach obcości kulturowej. Przypadek małoletnich uchodźców z Czeczenii w Polsce

2016 ◽  
Vol 60 (1) ◽  
pp. 93-118
Author(s):  
Katarzyna Kość-Ryżko
Keyword(s):  
Alternative Strategies ◽  
Model Based ◽  
Religious Identification ◽  
The Family ◽  
Sense Of Identity

Research conducted by the author in the years 2009–2014 among the children of refugees from Chechnya has shown that what is most important in terms of their functioning in the new culture occurs primarily in the family/ethnic environment, in the process of enculturation. This means that even though manifestations of progressing acculturation may be observed in the external sphere, this does not guarantee that the process is also occurring in the internal sphere of attitudes, convictions, and values. In this connection the writer’s attention was drawn to how under-age refugees from post-Soviet lands create a sense of identity and ethnic belonging. In particular, she considered the degree to which being a refugee and the situation in which these children find themselves have a formative influence on their self-identification. External indicators of ethnic, cultural, and religious identification were also analyzed. The author has thereby established the model—based on the two alternative strategies of reconstruction and deconstruction—by which young refugees create their self-identification.

Further Remarks on the Operational Nonterminal Complexity

2021 ◽  
pp. 1-15
Author(s):  
Jürgen Dassow
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Partial Result ◽  
Natural Numbers ◽  
Left Quotient

For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [2].

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