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Journal articles on the topic 'Lexicographical ordering'

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Author: Grafiati

Published: 6 September 2023

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1

Tung, Cheng-Tan. "Note on lexicographical ordering." International journal of Emerging Trends in Science and Technology 04, no. 05 (May 12, 2017): 5165–70. http://dx.doi.org/10.18535/ijetst/v4i5.06.

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2

Eghbali, Sepehr, and Ladan Tahvildari. "Test Case Prioritization Using Lexicographical Ordering." IEEE Transactions on Software Engineering 42, no. 12 (December 1, 2016): 1178–95. http://dx.doi.org/10.1109/tse.2016.2550441.

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3

Aptoula, E., and S. Lefèvre. "On lexicographical ordering in multivariate mathematical morphology." Pattern Recognition Letters 29, no. 2 (January 2008): 109–18. http://dx.doi.org/10.1016/j.patrec.2007.09.011.

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4

Lescanne, Pierre. "On the recursive decomposition ordering with lexicographical status and other related orderings." Journal of Automated Reasoning 6, no. 1 (March 1990): 39–49. http://dx.doi.org/10.1007/bf00302640.

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5

Er, M. C. "Lexicographical Ordering of k-Subsets of a Set." Journal of Information and Optimization Sciences 7, no. 2 (May 1986): 113–16. http://dx.doi.org/10.1080/02522667.1986.10698845.

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6

Cox, James L., Stephen Lucci, and Tayfun Pay. "Effects of Dynamic Variable - Value Ordering Heuristics on the Search Space of Sudoku Modeled as a Constraint Satisfaction Problem." Inteligencia Artificial 22, no. 63 (January 10, 2019): 1–15. http://dx.doi.org/10.4114/intartif.vol22iss63pp1-15.

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We carry out a detailed analysis of the effects of different dynamic variable and value ordering heuristics on the search space of Sudoku when the encoding method and the filtering algorithm are fixed. Our study starts by examining lexicographical variable and value ordering and evaluates different combinations of dynamic variable and value ordering heuristics. We eventually build up to a dynamic variable ordering heuristic that has two rounds of tie-breakers, where the second tie-breaker is a dynamic value ordering heuristic. We show that our method that uses this interlinked heuristic outperforms the previously studied ones with the same experimental setup. Overall, we conclude that constructing insightful dynamic variable ordering heuristics that also utilize a dynamic value ordering heuristic in their decision making process could drastically improve the search effort for some constraint satisfaction problems.

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7

MOU, Chen-qi. "Design of termination criterion of BMS algorithm for lexicographical ordering." Journal of Computer Applications 32, no. 11 (May 26, 2013): 2977–80. http://dx.doi.org/10.3724/sp.j.1087.2012.02977.

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8

Wu, Yaping, and Huiqing Liu. "Lexicographical ordering by spectral moments of trees with a prescribed diameter." Linear Algebra and its Applications 433, no. 11-12 (December 2010): 1707–13. http://dx.doi.org/10.1016/j.laa.2010.06.022.

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9

Fuertes-Olivera, Pedro A. "Specialised Lexicography for Learners: Specific Proposals for the Construction of Pedagogically-oriented Printed Business Dictionaries." HERMES - Journal of Language and Communication in Business 22, no. 42 (August 30, 2017): 167. http://dx.doi.org/10.7146/hjlcb.v22i42.96851.

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The function theory of lexicography argues that specialised lexicographical products must help learners to transform their information needs into aspects of knowledge of the discipline, and of its discursive properties. Lexicographers, then, must combine information and data access with the user’s need for information and knowledge. To achieve this aim they need to devise theories providing solutions to different lexicographical problems. One such theory has recently been proposed by Tarp (2008), who claims that there are four categories which are central to a general theory of learner’s lexicography: users, user situation, user needs, and dictionary assistance. This paper focuses on dictionary assistance and addresses several lexicographical issues connected with polysemy: the selection of the lemmata of some printed English-Spanish/Spanish-English business dictionaries, their entry structures, sense differentiation, and sense ordering. The analysis leads the author to discuss some proposals with the aim of making business dictionaries more pedagogically oriented, and to include a set of principles pedagogically-oriented business dictionaries must have. They are illustrated in a model entry which has been compiled by rearranging one of the entries studied according to the proposals and principles previously discussed.

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10

Farhadinia, B. "Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making." Information Sciences 327 (January 2016): 233–45. http://dx.doi.org/10.1016/j.ins.2015.07.057.

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11

Vazquez Noguera, Jose Luis, Christian E. Schaerer, Jacques Facon, and Horacio Legal Ayala. "Adaptive RGB Color Lexicographical Ordering Framework Using Statistical Parameters From the Color Component Histogram." IEEE Access 7 (2019): 141738–53. http://dx.doi.org/10.1109/access.2019.2943840.

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12

Cheng, Bo, and Bolian Liu. "Lexicographical ordering by spectral moments of trees with k pendant vertices and integer partitions." Applied Mathematics Letters 25, no. 5 (May 2012): 858–61. http://dx.doi.org/10.1016/j.aml.2011.10.032.

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13

Daciuk, Jan, Stoyan Mihov, Bruce W. Watson, and Richard E. Watson. "Incremental Construction of Minimal Acyclic Finite-State Automata." Computational Linguistics 26, no. 1 (March 2000): 3–16. http://dx.doi.org/10.1162/089120100561601.

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In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it. Our approach is to construct a minimal automaton in a single phase by adding new strings one by one and minimizing the resulting automaton on-the-fly. We present a general algorithm as well as a specialization that relies upon the lexicographical ordering of the input strings. Our method is fast and significantly lowers memory requirements in comparison to other methods.

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14

Fatichah, Chastine, Martin Leonard Tangel, Muhammad Rahmat Widyanto, Fangyan Dong, and Kaoru Hirota. "Interest-Based Ordering for Fuzzy Morphology on White Blood Cell Image Segmentation." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 1 (January 20, 2012): 76–86. http://dx.doi.org/10.20965/jaciii.2012.p0076.

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An Interest-based Ordering Scheme (IOS) for fuzzy morphology on White-Blood-Cell (WBC) image segmentation is proposed to improve accuracy of segmentation. The proposed method shows a high accuracy in segmenting both high- and low-density nuclei. Further, its running time is low, so it can be used for real applications. To evaluate the performance of the proposed method, 100 WBC images and 10 leukemia images are used, and the experimental results show that the proposed IOS segments a nucleus in WBC images 3.99% more accurately on average than the Lexicographical Ordering Scheme (LOS) does and 5.29% more accurately on average than the combined Fuzzy Clustering and Binary Morphology (FCBM) method does. The proposal method segments a cytoplasm 20.72% more accurately on average than the FCBM method. The WBC image segmentation is a part of WBC classification in an automatic cancer-diagnosis application that is being developed. In addition, the proposed method can be used to segment any images that focus on the important color of an object of interest.

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15

Mentynska, Iryna. "STAGES OF ESTABLISHMENT OF COMPUTER TERMINOLOGY AGAINST THE BACKGROUND OF THE DEVELOPMENT OF INFORMATION TECHNOLOGIES IN UKRAINE." Theory and Practice of Teaching Ukrainian as a Foreign Language, no. 17 (June 25, 2023): 181–90. http://dx.doi.org/10.30970/ufl.2023.17.3927.

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The article traces the formation of computer terminology against the background of the development of information technologies in Ukraine. Important stages of establishment of this field of knowledge are highlighted. Special attention is paid to the main lexicographical works, which became basic in the formation of the term system. The relevance of scientific research is determined by the need for a scientific description of the history of the development of Ukrainian computer terminology, as well as the need to determine the periodization of the formation of Ukrainian computer terminology. To realize the goal, the following tasks were completed1) describe the development of IT technologies in Ukraine; 2) the main stages of the adoption of computer terms against the background of the development of the computer industry are revealed; 3) lexicographical works that became basic in the formation of the computer sphere were carefully considered; 4) the peculiarities of the functioning of computer terms at each stage of development are established. The study of the history of the formation and development of industry terminology against the background of the development of information technologies in Ukraine makes it possible to determine the main regularities of the formation of the term system, to forecast the trends of its development using logical and linguistic ordering and a well-founded lexicographic description. The development and systematization of computer terminology are complex and ambiguous. We single out five important stages of the establishment of the computer industry against the background of the development of IT technologies in Ukraine: the 1st stage (beginning of the 20th century); 2nd (1941–1959); 3rd (1960-1989); 4th (1990–2000); 5th (early 2000 – until today). We trace that the emergence of information technologies in Ukraine dates back to 1914, however, due to intralingual and extra lingual factors, Ukrainian computer terminology developed sluggishly during the first and second periods. However, the fourth and fifth periods are characterized by rapid development and consistent systematization of the branch terminology. The main lexicographic works, which can be called basic in the formation of computer terminology, were the dictionaries of the 20 and 30 years of the 20th century. An important basis for establishing and codifying computer term units is the “Cybernetics Encyclopedia”, and at the current stage of development, online dictionaries of they IT. In the future, it would be worth investigating the stages of development of thermographic processing in the computer industry in Ukraine and abroad. Key words: terminology, term, computer terminology, computer technologies, lexicographic works.

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16

Sezan, Ibrahim. "Image Recovery Using Set-Theoretic Methods." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 1 (August 12, 1990): 446–47. http://dx.doi.org/10.1017/s0424820100180987.

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Recently, there is some interest in the application of set-theoretic methods to the solution of the image recovery problem in electron microscopy. Several current studies have reported promising results.The purpose of this paper is to introduce set-theoretic methods to the electron microscopy community.In electron microscopy, the image recovery problem refers to obtaining an estimate of the ideal three-dimensional (3-D) image distribution from its incomplete and possibly noisy Fourier transform data.In the spatial domain, the recovery problem is stated on the basis of the observation equation:where vectors g, f and n ∈ RN denote the lexicographical ordering of the (N-voxel) measured (degraded) image distribution, the ideal image distribution and the noise processes, respectively. The operator D : RN → RN denotes the degradation operator that effectively limits the data to the “data cone” in the frequency domain. The degradation operator can be adequately modeled by a space-invariant (convolutional) operator, and therefore D has a block-Toeplitz structure.

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Ristic, Stana, Ivana Lazic-Konjik, and Nenad Ivanovic. "The metalanguage of a lexicographic definition in the descriptive dictionary (based on the dictionaries of the Serbian language)." Juznoslovenski filolog 74, no. 1 (2018): 81–96. http://dx.doi.org/10.2298/jfi1801081r.

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In this paper we present the continuous hierarchical ordering of the first part of the definition of lexemes from the thematic group ?buildings? by analyzing the vertical organization of superordination of concepts in the lexicographical definition. We demonstrate that the vertical sequence mounts from a higher level of conceptual categorization, ?localizer,? in the form of complex and simple primitives (PLACE > SPACE [WHERE], SPACE > EXPANSE [SOMETHING THAT IS (BOUNDLESSLY) SPREADING IN EVERY DIRECTION]) and descends toward a lower hyperonimic level of ?buildings?. The suggested model links meanings systematically, on a micro-level of meaning within the polysemic structure, and on a macrolevel of meanings of lexemes belonging to a thematic group/class, which is significant for the descriptive lexicography and for the modeling of semantic description in the electronic dictionary of the contemporary Serbian language. Such description could facilitate the cross-referencing of lexemes and advanced search, which is essential both for linguists and dictionary users.

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18

König, Jason. "RE-READING POLLUX: ENCYCLOPAEDIC STRUCTURE AND ATHLETIC CULTURE IN ONOMASTICON BOOK 3." Classical Quarterly 66, no. 1 (May 2016): 298–315. http://dx.doi.org/10.1017/s0009838816000331.

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Ioulios Polydeukes, more commonly known as Pollux, was a Greek sophist and lexicographer active in the closing decades of the second century a.d. His Onomasticon is one of the most important lexicographical texts of the Imperial period. It is essentially a set of word lists dedicated to collecting clusters of related words on topics from a vast range of different areas of intellectual activity and everyday life. The text survives only in epitomized form, and shows signs of interpolation as well as abridgement. Nevertheless, the consensus is that the bulk of what survives is Pollux’ own work, and that reading it in Eric Bethe's Teubner edition gives an accurate cumulative impression of Pollux’ standard procedures and preoccupations, even if we cannot be entirely confident that any particular cluster of words had exactly the same form within the text's original design. It is divided into ten books, each with its own dedicatory preface addressed to the Emperor Commodus. Each book has its own distinctive focus on certain key themes, although the ordering principles are much clearer in some than in others.

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19

Melançon, Guy, and Christophe Reutenauer. "Lyndon Words, Free Algebras and Shuffles." Canadian Journal of Mathematics 41, no. 4 (August 1, 1989): 577–91. http://dx.doi.org/10.4153/cjm-1989-025-2.

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A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of the quotients of the lower central series of a free group or, equivalently, bases of the free Lie algebra [2], [7]. They have also many combinatorial properties, with applications to semigroups, pi-rings and pattern-matching, see [1], [10].We study here the Poincaré-Birkhoff-Witt basis constructed on the Lyndon basis (PBWL basis). We give an algorithm to write each word in this basis: it reads the word from right to left, and the first encountered inversion is either bracketted, or straightened, and this process is iterated: the point is to show that each bracketting is a standard one: this we show by introducing a loop invariant (property (S)) of the algorithm. This algorithm has some analogy with the collecting process of P. Hall [5], but was never described for the Lyndon basis, as far we know.

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20

BLOOM, S. L., and Z. ÉSIK. "ALGEBRAIC LINEAR ORDERINGS." International Journal of Foundations of Computer Science 22, no. 02 (February 2011): 491–515. http://dx.doi.org/10.1142/s0129054111008155.

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An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than ωω. It follows that the algebraic ordinals are exactly those less than ωωω.

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21

Martin, Ursula, and Elizabeth Scott. "The order types of termination orderings on monadic terms, strings and multisets." Journal of Symbolic Logic 62, no. 2 (June 1997): 624–35. http://dx.doi.org/10.2307/2275551.

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AbstractWe consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order typeω,ω2orωω. We show that a familiar construction gives rise to continuum many such orderings of order typeω. We construct a new family of such orderings of order typeω2, and show that there are continuum many of these. We show that there are only four such orderings of order typeωω, the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings onNnwhich are preserved under vector addition. We show that any such ordering must have order typeωkfor some 1 ≤k≤n. We show that ifk<nthere are continuum many such orderings, and ifk=nthere are onlyn!, then! lexicographic orderings.

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22

Semenova, Natalia V., Maria M. Lomaga, and Viktor V. Semenov. "LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD." Journal of Automation and Information sciences 1 (January 1, 2021): 30–40. http://dx.doi.org/10.34229/0572-2691-2021-1-3.

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The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

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23

Semenova, N. V., M. M. Lomaha, and V. V. Semenov. "Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions." Reports of the National Academy of Sciences of Ukraine, no. 12 (December 2020): 19–27. http://dx.doi.org/10.15407/dopovidi2020.12.019.

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Among vector problems, the lexicographic ones constitute a broad significant class of problems of optimization. Lexicographic ordering is applied to establish rules of subordination and priority. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under a risk, of the dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed the conditions of existence of solutions of multicriteria of lexicographic optimization problems with an unbounded set of feasible solutions on the basis of applying the properties of a recession cone of a con vex feasible set, the cone which puts it in order lexicographically with respect to optimization criteria. The obtained conditions may be successfully used while developing algorithms for finding the optimal solutions of the mentioned problems of lexicographic optimization. A method of finding the optimal solutions of convex lexico graphic problems with the linear functions of criteria is built and grounded on the basis of ideas of the method of linearization and the Kelley cutting plane method.

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24

COMON, HUBERT. "SOLVING SYMBOLIC ORDERING CONSTRAINTS." International Journal of Foundations of Computer Science 01, no. 04 (December 1990): 387–411. http://dx.doi.org/10.1142/s0129054190000278.

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We show how to solve boolean combinations of inequations s>t in the Herbrand Universe, assuming that ≥ is interpreted as a lexicographic path ordering extending a total precedence. In other words, we prove that the existential fragment of the theory of a lexicographic path ordering which extends a total precedence is decidable.

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25

Kazymyrova, Iryna. "ARCHITECTONICS OF THE REGISTER OF THE HISTORICAL DICTIONARY OF LINGUISTIC TERMS." Terminological Bulletin, no. 6 (2021): 172–79. http://dx.doi.org/10.37919/2221-8807-2021-6-16.

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The article is devoted to compiling a historical dictionary of linguistic terms, particularly the rules of the register’s organization. The importance of theoretical development of the principles of such a dictionary is emphasized, as the ordering of terminological systems should begin with the elucidation of the main tendencies of its historical evolution. One of the dictionary’s crucial components, which ensures access to the reader to the information contained in it, is its register. The article outlines the requirements for this fragment of the terminological dictionary. The scientific expediency of compiling a list of the historical dictionary of linguistic terms is caused by the fact that it will be carried out with its maximum fullness the complete registration of terminological units to denote the concepts of linguistics. An essential result of this work has become a register of the linguistic terms of the outlined period and establishing the theoretical principles of register representation of linguistic terms. In particular, the lexical material’s complexity would enable the organizing of the filling of the register, to reflect the terms variability, transfer in the register its system connections. Comprehensive fixation of the standard variants in the future will allow the compilation of word indexes to the individual linguistic sights. The corpus is based on the register part of the encyclopaedia Ukrainian Language. These are normative from the point of view of modern linguistics terms that represent the subject-logical and categorical-conceptual architecture of the linguistic terminological continuum, such as exclusive linguistic subcategories, crucial universal-linguistic concepts, basic general linguistic categories, unique linguistic super concepts, interdisciplinary linguistic concepts, and highly specialized linguistic concepts. Besides the main linguistic criteria, cultural, historical, literary, and ethnographic criteria for word selection and description are essential. Therefore, the register involves the representative word of modern linguistic terms and all its standard variants, selected from scientific, educational, and lexicographical sources. Filling the dictionary registry should consider that the pattern of variation in the Ukrainian language is very complex and ambiguous, due to the tracing and borrowing of linguistic terms, and instability of spelling rules.

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26

Law, Yat, Jimmy Lee, May Hiu Woo, and Toby Walsh. "A Comparison of Lex Bounds for Multiset Variables in Constraint Programming." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 61–67. http://dx.doi.org/10.1609/aaai.v25i1.7830.

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Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds according to one of the eight different orderings: length-(co)lex (LL/LC), variety-(co)lex (VL/VC), length-variety-(co)lex (LVL/LVC), and variety-length-(co)lex (VLL/VLC) orderings. These representations integrate together information about the cardinality, variety (number of distinct elements in the multiset), and position in some total ordering. Theoretical and empirical comparisons of expressiveness and compactness of the eight representations suggest that length-variety-(co)lex (LVL/LVC) and variety-length-(co)lex (VLL/VLC) usually give tighter bounds after constraint propagation. We implement the eight representations and evaluate them against the subset bounds representation with cardinality and variety reasoning. Results demonstrate that they offer significantly better pruning and runtime.

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27

Frisch, Alan M., Brahim Hnich, Zeynep Kiziltan, Ian Miguel, and Toby Walsh. "Propagation algorithms for lexicographic ordering constraints." Artificial Intelligence 170, no. 10 (July 2006): 803–34. http://dx.doi.org/10.1016/j.artint.2006.03.002.

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28

Stork, P., and J. M. Viaene. "Policy optimization by lexicographic preference ordering." Journal of Policy Modeling 14, no. 5 (October 1992): 655–73. http://dx.doi.org/10.1016/0161-8938(92)90035-b.

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29

Sadler, D. Royce. "Lexicographic Decision Rules and Selection for Higher Education." Australian Journal of Education 33, no. 2 (August 1989): 114–26. http://dx.doi.org/10.1177/168781408903300202.

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Currently in Australia, there is a strong demand for places in higher education. At the same time, a variety of methods of measuring and scaling secondary school achievements are used in the different states for making selection decisions, and these methods come under both professional and public scrutiny. A sequential screening procedure has recently been proposed in Queensland. It is based on what is known in decision theory as a ‘lexicographic ordering’. In this article, the concept of a lexicographic ordering is explained, and some of the associated assumptions, implications and shortcomings are examined. It is concluded that a lexicographic decision rule is unsuitable in its classical formulation as a procedure for selecting higher education entrants.

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30

Er, M. C. "Lexicographic ordering, ranking and unranking of combinations." International Journal of Computer Mathematics 17, no. 3-4 (January 1985): 277–83. http://dx.doi.org/10.1080/00207168508803468.

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31

Jee, Kyung-Wook, Daniel L. McShan, and Benedick A. Fraass. "Lexicographic ordering: intuitive multicriteria optimization for IMRT." Physics in Medicine and Biology 52, no. 7 (March 7, 2007): 1845–61. http://dx.doi.org/10.1088/0031-9155/52/7/006.

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32

Rizza, Davide. "Nonstandard utilities for lexicographically decomposable orderings." Journal of Mathematical Economics 60 (October 2015): 105–9. http://dx.doi.org/10.1016/j.jmateco.2015.06.012.

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33

Adams, Warren, Pietro Belotti, and Ruobing Shen. "Convex hull characterizations of lexicographic orderings." Journal of Global Optimization 66, no. 2 (April 25, 2016): 311–29. http://dx.doi.org/10.1007/s10898-016-0435-3.

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34

P, Phani Bushan Rao, and Ravi Shankar Nowpada. "Fuzzy Critical Path Method Based on Lexicographic Ordering." Pakistan Journal of Statistics and Operation Research 8, no. 1 (January 3, 2012): 139. http://dx.doi.org/10.18187/pjsor.v8i1.178.

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35

ÉSIK, ZOLTÁN. "ORDINAL AUTOMATA AND CANTOR NORMAL FORM." International Journal of Foundations of Computer Science 23, no. 01 (January 2012): 87–98. http://dx.doi.org/10.1142/s0129054112400060.

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It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than ωω. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial time algorithm to decide whether two deterministic finite automata accepting well-ordered regular languages accept isomorphic languages. We also give estimates on the state complexity of the smallest "ordinal automaton" representing an ordinal less than ωω, together with an algorithm that translates each such ordinal to an automaton.

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36

Krishnamurthy, E. V., and B. P. Vickers. "Compact numeral representation with combinators." Journal of Symbolic Logic 52, no. 2 (June 1987): 519–25. http://dx.doi.org/10.2307/2274398.

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AbstractThis paper is concerned with the combinator representation of numeral systems with logarithmic space complexity of symbols. The principle used is based on the lexicographic ordering of words over a finite alphabet.

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37

Conversano, Claudio, and Roberta Siciliano. "Incremental Tree-Based Missing Data Imputation with Lexicographic Ordering." Journal of Classification 26, no. 3 (December 2009): 361–79. http://dx.doi.org/10.1007/s00357-009-9038-8.

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38

Sergeyev, Yaroslav D. "The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities." Mathematical Intelligencer 37, no. 2 (January 1, 2015): 4–8. http://dx.doi.org/10.1007/s00283-014-9511-z.

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39

Saliba, Sleman. "Heuristics for the lexicographic max-ordering vehicle routing problem." Central European Journal of Operations Research 14, no. 3 (August 12, 2006): 313–36. http://dx.doi.org/10.1007/s10100-006-0007-6.

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Gupte, Akshay. "Convex hulls of superincreasing knapsacks and lexicographic orderings." Discrete Applied Mathematics 201 (March 2016): 150–63. http://dx.doi.org/10.1016/j.dam.2015.08.010.

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Zobnin, A. I. "One-element differential standard bases with respect to inverse lexicographical orderings." Journal of Mathematical Sciences 163, no. 5 (November 12, 2009): 523–33. http://dx.doi.org/10.1007/s10958-009-9690-x.

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Doğan, Battal, and Kemal Yildiz. "Choice with Affirmative Action." Management Science 69, no. 4 (April 2023): 2284–96. http://dx.doi.org/10.1287/mnsc.2022.4447.

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A choice rule with affirmative action decides on the recipients of a limited number of identical objects by reconciling two objectives: respecting a priority ordering over the applicants and supporting a minority group. We extend the standard formulation of a choice problem by incorporating a type function and a priority ordering and introduce monotonicity axioms on how a choice rule should respond to variations in these parameters. We show that monotonic and substitutable affirmative action rules are the ones that admit a bounded reserve representation. As a prominent class of choice rules that satisfy the monotonicity axioms, we characterize lexicographic affirmative action rules that are prevalent both in the literature and in practice. Our axiomatic approach provides a novel way to think about reserve systems and uncovers choice rules that go beyond lexicographic affirmative action rules. This paper was accepted by Yan Chen, behavioral economics and decision analysis. Funding: B. Doğan gratefully acknowledges financial support from the British Academy/Leverhulme Trust [Grant SRG1819\190133].

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Spoletini, E. "Generation of Permutations in Direct Lexicographic Ordering by Arithmetic Methods." Computer Journal 28, no. 4 (April 1, 1985): 444–45. http://dx.doi.org/10.1093/comjnl/28.4.444.

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Long, T., M. Matuszak, M. Feng, B. A. Fraass, R. K. Ten Haken, and H. E. Romeijn. "Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning." Medical Physics 39, no. 6Part1 (May 25, 2012): 3445–55. http://dx.doi.org/10.1118/1.4720218.

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Pak, D., M. Feng, E. Ben-Josef, R. Ten Haken, B. Fraass, and M. Matuszak. "Weighted Sum Cost Function Versus Lexicographic Ordering for IMRT Treatment Planning." International Journal of Radiation Oncology*Biology*Physics 84, no. 3 (November 2012): S795—S796. http://dx.doi.org/10.1016/j.ijrobp.2012.07.2128.

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Ziabicki, Andrzej. "The theory of ordering lexicographic entries: Principles, algorithms and computer implementation." Computers and the Humanities 26, no. 2 (April 1992): 119–37. http://dx.doi.org/10.1007/bf00116348.

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Genitrini, Antoine, and Martin Pépin. "Lexicographic Unranking of Combinations Revisited." Algorithms 14, no. 3 (March 19, 2021): 97. http://dx.doi.org/10.3390/a14030097.

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In the context of combinatorial sampling, the so-called “unranking method” can be seen as a link between a total order over the objects and an effective way to construct an object of given rank. The most classical order used in this context is the lexicographic order, which corresponds to the familiar word ordering in the dictionary. In this article, we propose a comparative study of four algorithms dedicated to the lexicographic unranking of combinations, including three algorithms that were introduced decades ago. We start the paper with the introduction of our new algorithm using a new strategy of computations based on the classical factorial numeral system (or factoradics). Then, we present, in a high level, the three other algorithms. For each case, we analyze its time complexity on average, within a uniform framework, and describe its strengths and weaknesses. For about 20 years, such algorithms have been implemented using big integer arithmetic rather than bounded integer arithmetic which makes the cost of computing some coefficients higher than previously stated. We propose improvements for all implementations, which take this fact into account, and we give a detailed complexity analysis, which is validated by an experimental analysis. Finally, we show that, even if the algorithms are based on different strategies, all are doing very similar computations. Lastly, we extend our approach to the unranking of other classical combinatorial objects such as families counted by multinomial coefficients and k-permutations.

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Louveau, Alain, and Jean Saint-Raymond. "On the quasi-ordering of Borel linear orders under embeddability." Journal of Symbolic Logic 55, no. 2 (June 1990): 537–60. http://dx.doi.org/10.2307/2274645.

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AbstractWe provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in Rω, with the lexicographic ordering. For Borel orders embeddable in R2, our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some Rn, n < ω, and hyperprojective determinacy for the general case.

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Kubat, Łukasz, and Jan Okniński. "Gröbner-Shirshov Bases for Plactic Algebras." Algebra Colloquium 21, no. 04 (October 6, 2014): 591–96. http://dx.doi.org/10.1142/s1005386714000534.

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A finite Gröbner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Gröbner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras.

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Comon, Hubert, and Ralf Treinen. "The first-order theory of lexicographic path orderings is undecidable." Theoretical Computer Science 176, no. 1-2 (April 1997): 67–87. http://dx.doi.org/10.1016/s0304-3975(96)00049-7.

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