The Book of Traces

Theory of traces

В цифровую эпоху в процессе автоматизации, роботизации различных отраслей производства и внедрения в него искусственного интеллекта используется уже трудно обозримое множество языков программирования. В результате в подготовке будущих инженеров все большое значение приобретает теория формальных языков, лежащая в основе разработки языков программирования. Незнание теории формальных языков стало причиной многих ошибок в разработке и использовании языков программирования в высокотехнологичных отраслях производства. Поэтому необходимо внедрение в содержание подготовки будущих инженеров дисциплины «Элементы теории формальных языков» для овладения ими теорией и практикой языков программирования. Установлено, что в методической литературе не разработаны эффективные методы обучения будущих инженеров формальным языкам. Цель статьи заключается в исследовании важных математических и методических аспектов обучения теории формальных языков будущих инженеров. Ведущую роль в исследовании играли методология дискретной математики и абстрактной алгебры, культурологический подход и методика преемственности в обучения между школой и вузом в содержании подготовки будущих инженеров. Результаты исследования. Охарактеризована культурологическая роль дискретной математики в современной теории формальных языков. На основе анализа избранных трудов В. М. Глушкова, Д. Кнута и других ученых исследована фундаментальная роль формальных языков абстрактной алгебры в обучении теории формальных языков. Охарактеризованы алгебраические аспекты методики обучения теории формальных языков и грамматик и роль в этой методике классических понятий абстрактной алгебры и их свойств. На основе этого изложены элементы методики преемственности в обучении элементам теории формальных языков будущих инженеров. В этих элементах важную роль играют различные трактовки понятия «язык» и примеры языков из математики и информатики. Раскрыта важная роль грамматик формальных языков в дальнейшем обучении этой теории. Результаты статьи имеют важное теоретическое и практическое значение в дальнейшем исследовании проблем методологии обучения будущих инженеров элементам теории формальных языков. Они представляют интерес для преподавателей, ведущих профессиональную подготовку студентов инженерных направлений в сфере автоматизации, роботизации отраслей производства и внедрения в него Искусственного интеллекта. In the digital era, in the process of automation, robotization of various industries and the introduction of Artificial Intelligence into it, numerous programming languages are widely applied. As a result, the theory of formal languages ​that underlies the development of programming languages is becoming increasingly important in the training of engineering students. The nescience of formal languages theory has caused many mistakes in the development and use of programming languages ​in high-tech industries. Therefore, it is necessary to introduce the discipline "Elements of the Theory of Formal Languages" into the content of the training of future engineers in order to master the theory and practice of programming languages. At the same time, it was established that the methodological literature hasn’t developed effective methods for teaching future engineers to formal languages. The purpose of the article is to investigate important mathematical and methodological aspects of teaching the theory of formal languages ​to engineering students. The leading role in the study was played by the methodology of discrete math and abstract algebra. Also, the cultural approach and the methodology of pre-graduation in training between school and university in the content of training future engineers. Findings.The cultural role of discrete mathematics in the modern theory of formal languages is determined in the article. Based on the analysis of selected works of V.M. Glushkov, D. Knut, and other scientists, the article investigates the fundamental role of formal languages ​of abstract algebra in teaching the theory of formal languages. Algebraic aspects of teaching methodology of the theory of formal languages ​and grammars, and the role in this methodology of classical concepts of abstract algebra and their propertieshave also become the subjects of the study. Basing on this, the elements of the methodology of continuity in teaching the elements of the theory of formal languages of future engineers are set out in the article. Various interpretations of the concept of "language" and examples of languages from mathematics, and computer science play an important role in these elements. The research also states the important role of grammars of formal languages in the further training of this theory. The findings of the research have important theoretical and practical significance in the further study of the issues of the methodology for teaching future engineers to the elements of the theory of formal languages. They are of interest to teachers conducting the professional training of engineering students in the field of automation, robotization of production industries, and the introduction of Artificial Intelligence into it.

We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our framework allows us to generalise standard constructions from the literature and to compare them. In particular, we consider notions such as global view, local view, and projections from the former to the latter. The correctness of local views projected from global views is characterised in terms of a closure property. We consider a number of communication properties -- such as (dead)lock-freedom -- and give conditions on formal choreographic languages to guarantee them. Finally, we show how formal choreographic languages can capture existing formalisms; specifically we consider communicating finite-state machines, choreography automata, and multiparty session types. Notably, formal choreographic languages, differently from most approaches in the literature, can naturally model systems exhibiting non-regular behaviour.

Closure properties of linear context-free tree languages with an application to optimality theory

THE INTERFACE BETWEEN LANGUAGE THEORY AND COMPLEXITY THEORY

Grammatical inference (also known as grammar induction) is a field transversal to a number of research areas including machine learning, formal language theory, syntactic and structural pattern recognition, computational linguistics, computational biology, and speech recognition. Specificities of the problems that are studied include those related to data complexity. We argue that there are three levels at which data complexity for grammatical inference can be studied: at the first (inner) level the data can be strings, trees, or graphs; these are nontrivial objects on which topologies may not always be easy to manage. A second level is concerned with the classes and the representations of the classes used for classification; formal language theory provides us with an elegant setting based on rewriting systems and recursivity, but which is not easy to work with for classification or learning tasks. The combinatoric problems usually attached to these tasks prove to be indeed difficult. The third level relates the objects to the classes. Membership may be problematic, and this is even more the case when approximations (of the strings or the languages) are used, for instance in a noisy setting. We argue that the main difficulties arise from the fact that the structural definitions of the languages and the topological measures do not match.

This is a paper on Stone duality in computer science with special focus on topics with applications in formal language theory. In Section 2 we give a general overview of Stone duality in its various forms: for Boolean algebras, distributive lattices, and frames. For distributive lattices, we discuss both Stone and Priestley duality. We identify how to move between the different dualities and which dual spaces carry the Scott topology. We then focus on three themes. The first theme is additional operations on distributive lattices and Boolean algebras. Additional operations arise in denotational semantics in the form of predicate transformers. In verification they occur in the form of modal operators. They play an essential role in Eilenberg's variety theorem in the form of quotient operations. Quotient operations are unary instantiations of residual operators which are dual to the operations in the profinite algebras of algebraic language theory. We discuss additional operations in Section 3. The second theme is that of hyperspaces, that is, spaces of subsets of an underlying space. Some classes of algebras may be seen as the class of algebras for a functor. In the case of predicate transformers the dual functors are hyperspace constructions such as the Plotkin, Smyth, and Hoare powerdomain constructions. The algebras-for-a-functor point of view is central to the coalgebraic study of modal logic and to the solution of domain In the algebraic theory of formal languages various hyperspace-related product constructions, such as block and Schutzenberger products, are used to study complexity hierarchies. We describe a construction, similar to the Schutzenberger product, which is dual to adding a layer of quantification to formulas describing formal languages. We discuss hyperspaces in Section 4. The final theme is that of equations. These are pairs of elements of dual spaces. They arise via the duality between subalgebras and quotient spaces and have provided one of the most successful tools for obtaining decidability results for classes of regular languages. The perspective provided by duality allows us to obtain a notion of equations for the study of arbitrary formal languages. Equations in language theory is the topic of Section 5.

Engaging and maintaining student engagement with the content of a course in formal language theory and the theory of computation is notoriously difficult. A major factor is student's perception of the relevance of the required mathematical material to computer science as they have studied the discipline. Usually, the mathematical material discourages students and for many it forms an insurmountable barrier. This paper describes the construction of a course using the discovery learning technique known as the Moore Method that directly addresses student engagement with this material. The results of the delivery of this course were that students remained engaged with the course throughout the semester and enthusiastically received the pedagogical approach employed. While the course described was delivered to a small class in a liberal arts college, it may be adapted to larger class sizes and taught in any computer science program.

The increasing complexity associated with many modern engineering applications, including autonomous robot guidance and navigation, process control in sensor-rich environments, and control of biological systems, has far-reaching implications for control system design. As an example, reactive, embedded software systems, interacting among themselves and remote users over communication networks, introduce a whole new set of system-level challenges, and classic control design objectives such as stability, performance, and robustness are being complemented with a number of new questions. These include the cost of hardware implementation, measured for example not only by computational requirements such as speed and memory, but also by communication requirements such as available communication bandwidth. Moreover, the complexity associated with specifying the control procedures and with verifying the behavior of the closed-loop system increasingly plays a fundamental role, especially in safety-critical control systems arising in energy and transportation networks, and in medical applications.

Symbol system is an important part of GIS system and CAD system. Analyzing the symbol systems of popular GIS systems and CAD systems, find out their merits and faults; and considering the requirement of geological field as mine and geological hazard, a vector-raster hybrid symbol system was designed. The paper introduced the main theory and key model of the symbol system, and introduced the advantages. And finally the fact is that the technology is feasible and could be widely used.

METHODS FOR SPECIFYING FAMILIES OF FORMAL LANGUAGES — PAST-PRESENT-FUTURE

Some connections between formal languages and complexity are reviewed. Families of formal languages are treated with complexity theoretical methods. In particular, the concept of unambiguity, common to both areas, is treated in detail. Some new results on deterministic families of formal languages and on complexities of operations on formal languages are indicated. >

The complexity of designing concurrent and highly-evolving interactive systems has grown to a point where system verification has become a hurdle. Fortunately, formal verification methods have arrived at the right time. They detect errors, inconsistencies and incompleteness at early development stages of a system formally modeled using a formal specification language. -calculus (Milner, 1999) is one such formal language which provides strong mathematical base that can be used for verifying system specifications. But manually verifying the specifications of concurrent systems is a very tedious and error-prone work, especially if the specifications are large. Consequently, an automated verification tool would be essential for efficient system design and development. In addition, formal verification tools are vital ingredient to fully harness the potential of component-based software composition. The authors developed such an automated verification tool which is highly portable and seamlessly integrates with the visualization, reduction and performance evaluation tools introduced (Ahmad & Rahimi, 2008; Rahimi, 2006; Rahimi et al., 2001, 2008) to provide a comprehensive tool for designing and analyzing multi process/agent systems. Open-Bisimulation (Sangiorgi, 1996) concept is utilized as the theoretical base for the design and implementation of the tool which incorporates an expert system implemented in Java Expert System Shell (JESS) (Friedman-Hill, 2003).

Toward a computational framework for cognitive biology: Unifying approaches from cognitive neuroscience and comparative cognition

Given that context-free grammars (CFG) cannot adequately describe natural languages, grammar formalisms beyond CFG that are still computationally tractable are of central interest for computational linguists. This book provides an extensive overview of the formal language landscape between CFG and PTIME, moving from Tree Adjoining Grammars to Multiple Context-Free Grammars and then to Range Concatenation Grammars while explaining available parsing techniques for these formalisms. Although familiarity with the basic notions of parsing and formal languages is helpful when reading this book, it is not a strict requirement. The presentation is supported with many illustrations and examples relating to the different formalisms and algorithms, and chapter summaries, problems and solutions. The book will be useful for students and researchers in computational linguistics and in formal language theory.