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Journal articles on the topic 'Algebraic automata theory'

Author: Grafiati

Published: 1 June 2024

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1

Pal, Priyanka, S. P. Tiwari, and Renu Verma. "Different Operators in Automata Theory Based on Residuated and Co-Residuated Lattices." New Mathematics and Natural Computation 15, no. 01 (2018): 169–90. http://dx.doi.org/10.1142/s1793005719500108.

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This paper is towards the algebraic and topological study of automata based on residuated and co-residuated lattices via different operators. The interrelationships among the operators are discussed. Interestingly, we show that the algebraic concepts of an automaton based on a residuated and co-residuated lattice can be expressed in terms of [Formula: see text]-topology/co-topology induced by operators. Finally, a composition of such automata is introduced and its categorical significance is discussed.

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2

Chilton, Chris, Bengt Jonsson, and Marta Kwiatkowska. "An algebraic theory of interface automata." Theoretical Computer Science 549 (September 2014): 146–74. http://dx.doi.org/10.1016/j.tcs.2014.07.018.

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Cadilhac, Michaël, Andreas Krebs, and Pierre McKenzie. "The Algebraic Theory of Parikh Automata." Theory of Computing Systems 62, no. 5 (2017): 1241–68. http://dx.doi.org/10.1007/s00224-017-9817-2.

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4

van Heerdt, Gerco, Joshua Moerman, Matteo Sammartino, and Alexandra Silva. "A (co)algebraic theory of succinct automata." Journal of Logical and Algebraic Methods in Programming 105 (June 2019): 112–25. http://dx.doi.org/10.1016/j.jlamp.2019.02.008.

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Novák, Michal, Štepán Křehlík, and Kyriakos Ovaliadis. "Elements of Hyperstructure Theory in UWSN Design and Data Aggregation." Symmetry 11, no. 6 (2019): 734. http://dx.doi.org/10.3390/sym11060734.

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In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying nodes or operating the network we, from the mathematical point of view, regard an operation (or a hyperoperation) and a binary relation. In this part of the paper we relate our context to already existing topics of the algebraic hyperstructure theory such as quasi-order hypergroups, E L -hyperstructures, or ordered hyperstructures. Furthermore, we make use of the theory o

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ANTIĆ, CHRISTIAN. "On Cascade Products of Answer Set Programs." Theory and Practice of Logic Programming 14, no. 4-5 (2014): 711–23. http://dx.doi.org/10.1017/s1471068414000301.

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AbstractDescribing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or “emulated”) by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept

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Derksen, Harm, Emmanuel Jeandel, and Pascal Koiran. "Quantum automata and algebraic groups." Journal of Symbolic Computation 39, no. 3-4 (2005): 357–71. http://dx.doi.org/10.1016/j.jsc.2004.11.008.

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Ambainis, Andris, Martin Beaudry, Marats Golovkins, Arnolds Kikusts, Mark Mercer, and Denis Therien. "Algebraic Results on Quantum Automata." Theory of Computing Systems 39, no. 1 (2005): 165–88. http://dx.doi.org/10.1007/s00224-005-1263-x.

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Pal, Priyanka, S. P. Tiwari, and J. Kavikumar. "Measure of Operators Associated with Fuzzy Automata." New Mathematics and Natural Computation 16, no. 01 (2020): 17–35. http://dx.doi.org/10.1142/s1793005720500027.

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This paper is toward the study of measure of different operators in fuzzy automata theory, which determine the amount of preciseness of given [Formula: see text]-valued subset endowed with an [Formula: see text]-valued preorder induced by [Formula: see text]-valued transition function of an [Formula: see text]-valued automaton. Further, we study the algebraic and topological study of [Formula: see text]-valued automata via different [Formula: see text]-valued operators and on the basis of homomorphism we examine the behavior of operators associated with an [Formula: see text]-valued automaton.

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LE SAEC, BERTRAND, JEAN-ERIC PIN, and PASCAL WEIL. "SEMIGROUPS WITH IDEMPOTENT STABILIZERS AND APPLICATIONS TO AUTOMATA THEORY." International Journal of Algebra and Computation 01, no. 03 (1991): 291–314. http://dx.doi.org/10.1142/s0218196791000195.

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Nous prouvons que tout semigroupe fini est quotient d'un semigroupe fini dans lequel les stabilisateurs droits satisfont les identités x = x2 et xy = xyx. Ce resultat a plusieurs consé-quences. Tout d'abord, nous l'utilisons, en même temps qu'un résultat de I. Simon sur les congruences de chemins, pour obtenir une preuve purement algébrique d'un théorème profond de McNaughton sur les mots infinis. Puis, nous donnons une preuve algébrique d'un théorème de Brown sur des conditions de finitude pour les semigroupes. We show that every finite semigroup is a quotient of a finite semigroup in which e

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Kalampakas, Antonios. "Graph Automata and Graph Colorability." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 112–20. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4629.

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Automata recognizing graphs can be constructed by employing the algebraic structure of graphoids. For the construction of a graph automaton, the relations over the Kleene star of the state set must constitute a graphoid. Hence different kinds of graphoids produce graph automata with diverse operation and recognition capacity. In this paper we show that graph colorability is recognized by automata operating over the simplest possible abelian graphoid.

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12

Kuich, Werner. "Pushdown Tree Automata, Algebraic Tree Systems, and Algebraic Tree Series." Information and Computation 165, no. 1 (2001): 69–99. http://dx.doi.org/10.1006/inco.2000.2908.

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13

Podlovchenko, R. I. "Finite state automata in the theory of algebraic program schemata." Proceedings of the Institute for System Programming of the RAS 27, no. 2 (2015): 161–72. http://dx.doi.org/10.15514/ispras-2015-27(2)-10.

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Kedlaya, Kiran S. "Finite automata and algebraic extensions of function fields." Journal de Théorie des Nombres de Bordeaux 18, no. 2 (2006): 379–420. http://dx.doi.org/10.5802/jtnb.551.

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Křehlík, Štěpán. "n-Ary Cartesian Composition of Multiautomata with Internal Link for Autonomous Control of Lane Shifting." Mathematics 8, no. 5 (2020): 835. http://dx.doi.org/10.3390/math8050835.

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In this paper, which is based on a real-life motivation, we present an algebraic theory of automata and multi-automata. We combine these (multi-)automata using the products introduced by W. Dörfler, where we work with the cartesian composition and we define the internal links among multiautomata by means of the internal links’ matrix. We used the obtained product of n-ary multi-automata as a system that models and controls certain traffic situations (lane shifting) for autonomous vehicles.

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Kim, S. H., and N. P. Suh. "Mathematical Foundations for Manufacturing." Journal of Engineering for Industry 109, no. 3 (1987): 213–18. http://dx.doi.org/10.1115/1.3187121.

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For the field of manufacturing to become a science, it is necessary to develop general mathematical descriptions for the analysis and synthesis of manufacturing systems. Standard analytic models, as used extensively in the past, are ineffective for describing the general manufacturing situation due to their inability to deal with discontinuous and nonlinear phenomena. These limitations are transcended by algebraic models based on set structures. Set-theoretic and algebraic structures may be used to (1) express with precision a variety of important qualitative concepts such as hierarchies, (2)

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Ebas, Nur Ain, Nor Shamsidah Amir Hamzah, Kavikumar Jacob, and Mohd Saifullah Rusiman. "Fuzzy Finite Switchboard Automata with Complete Residuated Lattices." International Journal of Engineering & Technology 7, no. 4.30 (2018): 160. http://dx.doi.org/10.14419/ijet.v7i4.30.22099.

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The theory of fuzzy finite switchboard automata (FFSA) is introduced by the use of general algebraic structures such as complete residuated lattices in order to enhance the process ability of FFSA. We established the notion of homomorphism, strong homomorphism and reverse homomorphism and shows some of its properties. The subsystem of FFSA is studied and the set of switchboard subsystem-forms a complete -sublattices is shown. The algorithm of FFSA with complete residuated lattices is given and an example is provided.

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Cardona, R., and N. Galatos. "The finite embeddability property for noncommutative knotted extensions of RL." International Journal of Algebra and Computation 25, no. 03 (2015): 349–79. http://dx.doi.org/10.1142/s0218196715500010.

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The finite embeddability property (FEP) for knotted extensions of residuated lattices holds under the assumption of commutativity, but fails in the general case. We identify weaker forms of the commutativity identity which ensure that the FEP holds. The results have applications outside of order algebra to non-classical logic, establishing the strong finite model property (SFMP) and the decidability for deductions, as well as to mathematical linguistics and automata theory, providing new conditions for recognizability of languages. Our proofs make use of residuated frames, developed in the con

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19

Letychevskyi, Oleksandr. "Algebraic School of V.M. Glushkov and Insertion Modeling." Cybernetics and Computer Technologies, no. 4 (December 4, 2023): 8–15. http://dx.doi.org/10.34229/2707-451x.23.4.2.

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The Algebraic School of Viktor Mykhailovych Glushkov already has several generations of scientists, most of whom have already identified and are developing their own scientific directions. This school, started at the Institute of Cybernetics, was shaped by research that had the significance of inventions at the level of world science and the computer industry and in many ways predicted their further development. The work considers the formation of the paradigm of insertion modeling as a generalization of the main achievements of the Glushkov school, starting from the theory of automata and up

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Comin, Carlo. "Algebraic Characterization of the Class of Languages Recognized by Measure Only Quantum Automata." Fundamenta Informaticae 134, no. 3-4 (2014): 335–53. http://dx.doi.org/10.3233/fi-2014-1105.

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21

Semerenko, Vasyl, and Oleksandr Voinalovich. "The simplification of computationals in error correction coding." Technology audit and production reserves 3, no. 2(59) (2021): 24–28. http://dx.doi.org/10.15587/2706-5448.2021.233656.

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The object of research is the processes of error correction transformation of information in automated systems. The research is aimed at reducing the complexity of decoding cyclic codes by combining modern mathematical models and practical tools. The main prerequisite for the complication of computations in deterministic linear error-correcting codes is the use of the algebraic representation as the main mathematical apparatus for these types of codes. Despite the universalism of the algebraic approach, its main drawback is the impossibility of taking into account the characteristic features o

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22

Jin, Jianhua, Qingguo Li, and Chunquan Li. "On Intuitionistic Fuzzy Context-Free Languages." Journal of Applied Mathematics 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/825249.

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Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset construction method, we show that IFPDAs are equivalent to their simple form, called intuitionistic fuzzy simple pushdown automata (IF-SPDAs), and then prove that intuitionistic fuzzy recognizable step fu

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23

Chen, Yu-Fang, Kai-Min Chung, Ondřej Lengál, Jyun-Ao Lin, Wei-Lun Tsai, and Di-De Yen. "An Automata-Based Framework for Verification and Bug Hunting in Quantum Circuits." Proceedings of the ACM on Programming Languages 7, PLDI (2023): 1218–43. http://dx.doi.org/10.1145/3591270.

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We introduce a new paradigm for analysing and finding bugs in quantum circuits. In our approach, the problem is given by a ‍triple { P } C { Q } and the question is whether, given a set P of quantum states on the input of a circuit C , the set of quantum states on the output is equal to (or included in) a set Q . While this is not suitable to specify, e.g., functional correctness of a quantum circuit, it is sufficient to detect many bugs in quantum circuits. We propose a technique based on tree automata to compactly represent sets of quantum states and develop transformers to implement the sem

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Attou, Samira, Ludovic Mignot, Clément Miklarz, and Florent Nicart. "Monadic Expressions and Their Derivatives." RAIRO - Theoretical Informatics and Applications 58 (2024): 6. http://dx.doi.org/10.1051/ita/2023014.

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There are several well-known ways to compute derivatives of regular expressions due to Brzozowski, Antimirov or Lombardy and Sakarovitch. We propose another one which abstracts the underlying data structures (e.g. sets or linear combinations) using the notion of monad. As an example of this generalization advantage, we first introduce a new derivation technique based on the graded module monad and then show an application of this technique to generalize the parsing of expressions with capture groups and back references. We also extend operators defining expressions to any n-ary functions over

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25

Gulistan, Muhammad, Feng Feng, Madad Khan, and Aslıhan Sezgin. "Characterizations of Right Weakly Regular Semigroups in Terms of Generalized Cubic Soft Sets." Mathematics 6, no. 12 (2018): 293. http://dx.doi.org/10.3390/math6120293.

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Cubic sets are the very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [ 0 , 1 ] and a number from [ 0 , 1 ] . Generalized cubic sets generalized the cubic sets with the help of cubic point. On the other hand Soft sets were proved to be very effective tool for handling imprecision. Semigroups are the associative structures have many applications in the theory of Automata. In this paper we blend the idea of cubic sets, generalized cubic sets and semigroups with the soft sets in order to develop a generalized approach namely generalized cub

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Bystrova, I. V., and B. P. Podkopaev. "Fault Isolation in Network of State Automates." Journal of the Russian Universities. Radioelectronics 23, no. 1 (2020): 18–29. http://dx.doi.org/10.32603/1993-8985-2020-23-1-18-29.

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Introduction. In the paper a fault isolation problem in the devices combining digital unit by functional diagnostics methods is considered. Networks of state automates are accepted as mathematical models of the devices. Assumed, that functional diagnostics devices for each network component are preliminarily constructed in an optimal way and they consist of a control automata and of a fault discriminator of unit dimension.Aim. To develop functional diagnostics method based on theoretical analysis allowing to decide fault isolation problem in networks of state automation and to reduce computati

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Denis, Laurent. "Méthodes fonctionnelles pour la transcendance en caractéristique finie." Bulletin of the Australian Mathematical Society 50, no. 2 (1994): 273–86. http://dx.doi.org/10.1017/s0004972700013733.

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There are essentially two ways to obtain transcendence results in finite characteristic. The first, historically, is to use Ore's lemma and to prove that a series whose coefficients satisfy well-behaved divisibility properties cannot be a zero of an additive polynomial. This method is of the same kind as the method of p–automata. The second one is to try to imitate the usual methods in characteristic zero and to do transcendence theory with t–modules analogously to what we can do with algebraic groups. We want to show here that transcendence results over Fq(T) can also be obtained with the hel

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Jones, Nick G., and Noah Linden. "Integrable spin chains and the Clifford group." Journal of Mathematical Physics 63, no. 10 (2022): 101901. http://dx.doi.org/10.1063/5.0095870.

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We construct new families of spin chain Hamiltonians that are local, integrable, and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford group transformations that can be described by matrix product operators (MPOs). We classify translation invariant Clifford group transformations that consist of a shift operator and an MPO of bond dimension two—this includes transformations that preserve locality of all Hamiltonians and those that lead to non-local images of particular operators but, never

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KÁDÁR, ZOLTÁN, ANNALISA MARZUOLI, and MARIO RASETTI. "BRAIDING AND ENTANGLEMENT IN SPIN NETWORKS: A COMBINATORIAL APPROACH TO TOPOLOGICAL PHASES." International Journal of Quantum Information 07, supp01 (2009): 195–203. http://dx.doi.org/10.1142/s0219749909004785.

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The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q = root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin network automata are able to perform efficiently approximate calculations of topological invarians of knots and 3-manifolds. The same algebraic background is shared by 2D lattice models supporting topological phases of matter that have recently gained much interest in condensed matter physics. These developments are motivated by the possibility to store qu

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Picantin, Matthieu. "Automatic Structures for Torus Link Groups." Journal of Knot Theory and Its Ramifications 12, no. 06 (2003): 833–66. http://dx.doi.org/10.1142/s0218216503002627.

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A general result of Epstein and Thurston implies that all link groups are automatic, but the proof provides no explicit automaton. Here we show that the groups of all torus links are groups of fractions of so-called Garside monoids, i.e., roughly speaking, monoids with a good theory of divisibility, which allows us to reprove that those groups are automatic, but, in addition, gives a completely explicit description of the involved automata, thus partially answering a question of D. F. Holt.

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Gornev, E. S., and I. V. Matyushkin. "A discussion of S.M. Krylov’s book «Neocybernetics» (2008)." Russian Technological Journal 9, no. 6 (2021): 73–87. http://dx.doi.org/10.32362/2500-316x-2021-9-6-73-87.

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A comparative analysis of the “general formal technology (GFT)” by S. M. Krylov is carried out in the context of the published book of the authors “General Theory of Technologies and Microelectronics” (2020) and on the basis of his work of 2008. Despite the abstractness of the algebraic-algorithmic approach, Krylov offers a number of specific constructions that are in demand during the fourth industrial revolution and for the future development of industrial technology in nanoelectronics and biotechnology. Industrial technology is considered as a complex object of management, i.e., it is the o

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32

Гайдур, Галина Іванівна, Сергій Олександрович Гахов та Віталій Вікторович Марченко. "Метод побудови динамічної моделі логічного об’єкта інформаційної системи та визначення закону його функціонування". RADIOELECTRONIC AND COMPUTER SYSTEMS, № 1 (23 лютого 2022): 129–40. http://dx.doi.org/10.32620/reks.2022.1.10.

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The subject of the research in this article is the methods for detecting intrusions into the information systems of organizations to justify the requirements for the functioning of the monitoring agent of the selected logical object. The aim is to develop a method for building a dynamic model of the logical object of the information system and determine the law of its operation. Tasks: to substantiate the need to create security monitoring agents for logical objects of information systems; identify the main functions of security monitoring agents for logical objects; to propose a method for bu

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Brieussel, Jérémie. "An automata group of intermediate growth and exponential activity." Journal of Group Theory 21, no. 4 (2018): 573–78. http://dx.doi.org/10.1515/jgth-2017-0046.

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AbstractWe give a new example of an automata group of intermediate growth. It is generated by an automaton with four states on an alphabet with eight letters. This automata group has exponential activity and its limit space is not simply connected.

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Wiweger, Antoni. "Free Games over Coloured Automata." Fundamenta Informaticae 8, no. 2 (1985): 199–224. http://dx.doi.org/10.3233/fi-1985-8204.

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Concepts of category theory are applied to the investigation of some relations between automata and abstract games. The notion of a coloured automaton introduced in this paper provides a framework for a unified treatment of automata and abstract games. Both games and automata can be viewed as special cases of this general notion. A coloured automaton is defined to be a Mealy automaton with the additional structure of a coloured graph on the set of inputs. Various categories of coloured automata, automata, and games are described. It is shown that some forgetful functors between these categorie

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Champarnaud, J. M., and G. Hansel. "AUTOMATE, a computing package for automata and finite semigroups." Journal of Symbolic Computation 12, no. 2 (1991): 197–220. http://dx.doi.org/10.1016/s0747-7171(08)80125-3.

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D'Angeli, Daniele, Dominik Francoeur, Emanuele Rodaro, and Jan Philipp Wächter. "On the orbits of automaton semigroups and groups." Algebra and Discrete Mathematics 33, no. 1 (2022): 1–29. http://dx.doi.org/10.12958/adm1692.

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We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivalent to the finiteness problem for left principal ideals in automaton semigroups generated by complete and reversible automata. Then, we look at w-word (i.\,e.\ right infinite words) with a finite orbit. We show that every automaton yielding an w-word with a finite orbit already yields an ultimately

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FABERT, OLIVER. "LOCAL SYMPLECTIC FIELD THEORY." International Journal of Mathematics 24, no. 05 (2013): 1350041. http://dx.doi.org/10.1142/s0129167x13500419.

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Generalizing local Gromov–Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and discuss the resulting algebraic structures.

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Peltier, Nicolas. "Tree Automata and Automated Model Building." Fundamenta Informaticae 30, no. 1 (1997): 59–81. http://dx.doi.org/10.3233/fi-1997-30105.

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Martiník, Ivo. "Automation of Presentation Record Production Based on Rich-Media Technology Using SNT Petri Nets Theory." Scientific World Journal 2015 (2015): 1–19. http://dx.doi.org/10.1155/2015/303705.

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Rich-media describes a broad range of digital interactive media that is increasingly used in the Internet and also in the support of education. Last year, a special pilot audiovisual lecture room was built as a part of the MERLINGO (MEdia-rich Repository of LearnING Objects) project solution. It contains all the elements of the modern lecture room determined for the implementation of presentation recordings based on the rich-media technologies and their publication online or on-demand featuring the access of all its elements in the automated mode including automatic editing. Property-preservin

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Dunets, Andriy, Gerhard Schellhorn, and Wolfgang Reif. "Automated Flaw Detection in Algebraic Specifications." Journal of Automated Reasoning 45, no. 4 (2010): 359–95. http://dx.doi.org/10.1007/s10817-010-9166-1.

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Ganty, Pierre, Elena Gutiérrez, and Pedro Valero. "A Congruence-Based Perspective on Finite Tree Automata." Fundamenta Informaticae 184, no. 1 (2022): 1–47. http://dx.doi.org/10.3233/fi-2021-2091.

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We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the redu

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Otto, Friedrich. "A Complete Taxonomy of Restarting Automata without Auxiliary Symbols*." Fundamenta Informaticae 180, no. 1-2 (2021): 77–101. http://dx.doi.org/10.3233/fi-2021-2035.

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A complete taxonomy is presented for restarting automata without auxiliary symbols. In this taxonomy, the language classes that are accepted by deterministic and nondeterministic, monotone, weakly monotone, and non-monotone, shrinking and length-reducing restarting automata are compared to each other with respect to inclusion. As it turns out, the 45 types of restarting automata considered yield 29 different classes of languages. By presenting a collection of rather simple example languages, it is shown that, for any two of these language classes ℒ1 and ℒ2, the class ℒ1 is a subclass of ℒ2 if

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Kutylowski, Miroslaw. "Chains of Finite Automat a with Bounded Number of Chains1." Fundamenta Informaticae 11, no. 3 (1988): 267–73. http://dx.doi.org/10.3233/fi-1988-11304.

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Chains of finite automata are considered. We show that if the lowest automaton in a chain controls movements of the common reading head then computing power of the chain is very limited. This is a generalization of Krohn-Rhodes theorem on one-way automata.

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Löding, Christof, та Max Philip Stachon. "On Minimization and Learning of Deterministic ω-Automata in the Presence of Don’t Care Words". Fundamenta Informaticae 189, № 1 (2023): 69–91. http://dx.doi.org/10.3233/fi-222152.

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We study minimization problems for deterministic ω-automata in the presence of don’t care words. We prove that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don’t care words. We derive that from a more general result from which one also obtains an efficient minimization algorithm for deterministic parity automata with informative right-congruence (without don’t care words). We then analyze languages of don’t care words with a trivial right-congruence. For such sets of don’t care words it is known that weak deterministic Büchi a

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Fernau, Henning, Martin Kutrib, and Matthias Wendlandt. "Self-Verifying Pushdown and Queue Automata." Fundamenta Informaticae 180, no. 1-2 (2021): 1–28. http://dx.doi.org/10.3233/fi-2021-2032.

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We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that SVPDA and SVRQA are automata characterizations of so-called complementation kernels, that is, context-free

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Pighizzini, Giovanni, and Luca Prigioniero. "Non-Self-Embedding Grammars and Descriptional Complexity." Fundamenta Informaticae 180, no. 1-2 (2021): 103–22. http://dx.doi.org/10.3233/fi-2021-2036.

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Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. In particular, each non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size

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Černý, Anton, and Jozef Gruska. "Modular Real-Time Trellis Automata." Fundamenta Informaticae 9, no. 3 (1986): 253–82. http://dx.doi.org/10.3233/fi-1986-9302.

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A new type of nonhomogeneous real time trellis automata, the so-called modular trellis automata, is introduced and various results concerning their normal forms, power, simulations, and decision problems are shown. Modular trellis automata are a mathematical abstraction, in the form of a recognizer, of an intuitive notion of an array of simple processors assembled in a simple and modular way. Distribution of processors in a real-time trellis automaton forms a two-dimensional structure called trellis. Basic characterizations and properties of modular trellises are summarized and modularity of v

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Beyne, Tim, and Michiel Verbauwhede. "Integral Cryptanalysis Using Algebraic Transition Matrices." IACR Transactions on Symmetric Cryptology 2023, no. 4 (2023): 244–69. http://dx.doi.org/10.46586/tosc.v2023.i4.244-269.

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In this work we introduce algebraic transition matrices as the basis for a new approach to integral cryptanalysis that unifies monomial trails (Hu et al., Asiacrypt 2020) and parity sets (Boura and Canteaut, Crypto 2016). Algebraic transition matrices allow for the computation of the algebraic normal form of a primitive based on the algebraic normal forms of its components by means of wellunderstood operations from linear algebra. The theory of algebraic transition matrices leads to better insight into the relation between integral properties of F and F−1. In addition, we show that the link be

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Dobronravov, Egor, Nikita Dobronravov, and Alexander Okhotin. "On the Length of Shortest Strings Accepted by Two-way Finite Automata." Fundamenta Informaticae 180, no. 4 (2021): 315–31. http://dx.doi.org/10.3233/fi-2021-2044.

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Given a two-way finite automaton recognizing a non-empty language, consider the length of the shortest string it accepts, and, for each n ≥ 1, let f(n) be the maximum of these lengths over all n-state automata. It is proved that for n-state two-way finite automata, whether deterministic or nondeterministic, this number is at least Ω(10n/5) and less than (2nn+1), with the lower bound reached over an alphabet of size Θ(n). Furthermore, for deterministic automata and for a fixed alphabet of size m ≥ 1, the length of the shortest string is at least e(1+o(1))mn(log n− log m).

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Sakai, Masahiko, Toshiki Sakabe, and Yasuyoshi Inagaki. "Algebraic specification and automatic generation of compilers." Systems and Computers in Japan 23, no. 2 (1992): 1–13. http://dx.doi.org/10.1002/scj.4690230201.

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