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A Structural Lemma for Deterministic Context-Free Languages
P. 553–565.
Rubtsov A. A.
We present a new structural lemma for deterministic con- text free languages. From the first sight, it looks like a pumping lemma, because it is also based on iteration properties, but it has significant distinctions that makes it much easier to apply. The structural lemma is a combinatorial analogue of KC-DCF-Lemma (based on Kolmogorov complexity), presented by Li and Vit ́anyi in 1995 and corrected by Glier in 2003. The structural lemma allows not only to prove that a language is not a DCFL, but discloses the structure of DCFLs Myhill-Nerode classes.
Keywords: колмогоровская сложностьKolmogorov complexityтеория автоматовautomata theoryформальные языкиformal languages
Publication based on the results of:
Semenov A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 527 № S С. 7–12
The paper proposes a system of definitions for the basic concepts of computability theory that underlie the mathematics of the digital world: algorithm, computability, calculus, object complexity, close to modern undertnding. Hierarchies of the finite and the problem of consistency are considered. ...
Added: December 6, 2025
Semenov A., Shen A., Vereshchagin N., Theory of Probability and its Applications, USA 2024 Vol. 68 No. 4 P. 582–606
The definition of descriptional complexity of finite objects suggested by Kolmogorov and other authors in the mid-1960s is now well known. In addition, Kolmogorov pointed out some approaches to a more fine-grained classification of finite objects, such as the resource-bounded complexity (1965), structure function (1974), and the notion of $(\alpha,\beta)$-stochasticity (1981). Later it turned out ...
Added: January 16, 2025
Vereshchagin N., / Series arXiv "math". 2024.
The fine approach to measure information dependence is based on the total conditional complexity CT(y|x), which is defined as the minimal length of a total program that outputs y on the input x. It is known that the total conditional complexity can be much larger than than the plain conditional complexity. Such strings x, y ...
Added: August 19, 2024
М.: Московский государственный технический университет им. Н.Э. Баумана, 2023.
Сборник содержит тезисы докладов, представленных на международной научно-технической конференции "Безопасные информационные технологии" (БИТ-2023), проходившей 1-2 ноября 2023 г. в Москве в МГТУ им. Н.Э.Баумана.
Тезисы публикуются в редакции научных руководителей или в авторской редакции при наличии ученой степени. ...
Added: February 16, 2024
Sergey Dudakov, Karlov B., Theory of Computing Systems 2021 Vol. 65 No. 3 P. 462–478
This paper is dedicated to studying decidability properties of theories of regular languages with classical operations: union, concatenation, and the Kleene star. The theory with union only is a theory of some Boolean algebra, so it is decidable. We prove that the theory of regular languages with the Kleene star only is decidable. If we ...
Added: November 12, 2023
Дехтярь М. И., Dudakov S., Карлов Б. Н., Тверь: Тверской государственный университет, 2021.
Учебное пособие адресовано изучающим курс дискретной математики, прежде всего, студентам младших курсов, обучающимся по направлениям укрупненных групп 01.03.00 "Математика и механика", 02.03.00 "Компьютерные и информационные науки", 09.03.00 "Информатика и вычислительная техника".
Настоящий сборник задач является пособием для практических занятий по некоторым разделам дискретной математики и может быть использован преподавателями и студентами для подготовки к семинарским занятиям и ...
Added: November 12, 2023
Мещеряков М. В., Сухарев Л. А., Саранск: Изд-во Мордовского университета, 2018.
The book is an introductory course on the theory of formal languages and finite automata. It presents the main material of diciplina related to the mathematical foundations of a number of syntactic methods of inormatics and programming. The book is intended for undergraduate students in the following fields of study: fundamental computer science and information ...
Added: October 12, 2023
Bauwens B. F., Zimand M., Journal of the ACM 2023 Vol. 70 No. 2 Article 9
In a lossless compression system with target lengths, a compressor 𝒞 maps an integer m and a binary string x to an m-bit code p, and if m is sufficiently large, a decompressor 𝒟 reconstructs x from p. We call a pair (m,x) achievable for (𝒞,𝒟) if this reconstruction is successful. We introduce the notion ...
Added: March 22, 2023
Bauwens B. F., Gács P., Romashchenko A. et al., Computability 2022 Vol. 11 No. 3-4 P. 165–185
Finding all linear inequalities for entropies remains an important open question in information theory. For a long time the only known inequalities for entropies of tuples of random variables were Shannon (submodularity) inequalities. Only in 1998 Zhang and Yeung 1998 found the first inequality that cannot be represented as a convex combination of Shannon inequalities, and ...
Added: December 23, 2022
Vereshchagin N., Theoretical Computer Science 2023 Vol. 940 P. 108–122
We consider the network consisting of three nodes 1, 2, 3 connected by two open channels
1 → 2 and 1 → 3. The information present in the node 1 consists of four strings x , y , z , w.
The nodes 2, 3 know x , w and need to know y , z, respectively. ...
Added: December 19, 2022
Govindaraj R., Mahendran A., International Journal of Reasoning-based Intelligent Systems 2018 Vol. 3 No. 4 P. 197–203
A picture grammar is the generation of pictures through description of words. The picture is represented in matrix form of finite alphabet using various grammars. Picture grammar can be achieved through context free grammar or regular expressions. Here we extend hexagonal picture language to octagonal picture language thereby introducing octagonal Wang system (OWS) and octagonal ...
Added: November 24, 2021
Babash A. V., , in: Proceedings of the 10th International Scientific and Practical Conference named after A. I. Kitov "Information Technologies and Mathematical Methods in Economics and Management (IT&MM-2020)"/, Moscow, Russia, October 15-16, 2020Vol. 2830.: CEUR Workshop Proceedings, 2021. P. 337–359.
A trapdoor cipher is a cipher whose algorithm contains some hidden structure (a trapdoor) providing the existence of a subliminal information channel. In cryptographic practice, there could be situations when a constructed cipher may contain some critical defect (a trapdoor) whose identification can significantly weaken the cryptographic strength of this cipher. In this paper, we ...
Added: November 2, 2021
Switzerland: Springer International Publishing, 2021.
Added: September 28, 2021
Milovanov A., , in: Computer Science – Theory and Applications: 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28–July 2, 2021, Proceedings.: Springer, 2021. Ch. 17 P. 283–295.
We combine Solomonoff’s approach to universal prediction with algorithmic statistics and suggest to use the computable measure that provides the best “explanation” for the observed data (in the sense of algorithmic statistics) for prediction. In this way we keep the expected sum of squares of prediction errors bounded (as it was for the Solomonoff’s predictor) ...
Added: August 11, 2021
Bauwens B. F., Blinnikov I., , in: Computer Science – Theory and Applications 15th International Computer Science Symposium in Russia, CSR 2020, Yekaterinburg, Russia, June 29 – July 3, 2020, ProceedingsVol. 12159.: Springer, 2020. P. 130–141.
It is known that the normalized algorithmic information distance is not computable and not semicomputable. We show that for all 𝜀<1/2, there exist no semicomputable functions that differ from N by at most 𝜀. Moreover, for any computable function f such that |lim𝑡𝑓(𝑥,𝑦,𝑡)−N(𝑥,𝑦)|≤𝜀 and for all n, there exist strings x, y of length n such that ...
Added: February 5, 2021
Cham: Springer, 2020.
This Festschrift is in honor of Prof. Andre Scedrov at the University of Pennsylvania. Scedrov has laid the foundations for a number of now well-established domains in mathematics and computer science including Proof Theory, Logic in Computer Science, Foundations in Computer Security, and Linguistics.
This combination of breadth and penetrating originality is rare and impressive. This ...
Added: November 25, 2020
Chistikov D., Mikhail Vyalyi, , in: LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science. Saarbrücken, Germany. July, 2020.: Association for Computing Machinery (ACM), 2020. P. 312–326.
Added: September 4, 2020
Bauwens B. F., , in: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)Vol. 154: Leibniz International Proceedings in Informatics (LIPIcs).: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2020. P. 46:1–46:14.
Added: March 20, 2020
Vereshchagin N., Theoretical Computer Science 2020 Vol. 809 P. 531–537
The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the following two complexities of an infinite computable 0-1-sequence $\alpha$: $C^{0'}(\alpha )$, defined as ...
Added: January 17, 2020
Grigorev S., Bozhko S., Хатбуллина Л. Р., Lecture Notes in Computer Science 2019 Vol. 11541 P. 264–281
Formal language theory has a deep connection with such areas as static code analysis, graph database querying, formal verifica- tion, and compressed data processing. Many application problems can be formulated in terms of languages intersection. The Bar-Hillel theo- rem states that context-free languages are closed under intersection with a regular set. This theorem has a ...
Added: August 20, 2019