Codes And Automata

This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

All aboard The Coding Train! This beginner-friendly creative coding tutorial is designed to grow your skills in a fun, hands-on way as you build simulations of real-world phenomena with “The Coding Train” YouTube star Daniel Shiffman. What if you could re-create the awe-inspiring flocking patterns of birds or the hypnotic dance of fireflies—with code? For over a decade, The Nature of Code has empowered countless readers to do just that, bridging the gap between creative expression and programming. This innovative guide by Daniel Shiffman, creator of the beloved Coding Train, welcomes budding and seasoned programmers alike into a world where code meets playful creativity. This JavaScript-based edition of Shiffman’s groundbreaking work gently unfolds the mysteries of the natural world, turning complex topics like genetic algorithms, physics-based simulations, and neural networks into accessible and visually stunning creations. Embark on this extraordinary adventure with projects involving: A physics engine: Simulate the push and pull of gravitational attraction. Flocking birds: Choreograph the mesmerizing dance of a flock. Branching trees: Grow lifelike and organic tree structures. Neural networks: Craft intelligent systems that learn and adapt. Cellular automata: Uncover the magic of self-organizing patterns. Evolutionary algorithms: Play witness to natural selection in your code. Shiffman’s work has transformed thousands of curious minds into creators, breaking down barriers between science, art, and technology, and inviting readers to see code not just as a tool for tasks but as a canvas for boundless creativity. Whether you’re deciphering the elegant patterns of natural phenomena or crafting your own digital ecosystems, Shiffman’s guidance is sure to inform and inspire. The Nature of Code is not just about coding; it’s about looking at the natural world in a new way and letting its wonders inspire your next creation. Dive in and discover the joy of turning code into art—all while mastering coding fundamentals along the way. NOTE: All examples are written with p5.js, a JavaScript library for creative coding, and are available on the book's website.

Theory of Codes

The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices.Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole.Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.

Algorithms, Languages, Automata, & Compilers A Practical Approach is designed to cover the standard “theory of computing” topics through a strong emphasis on practical applications rather than theorems and proofs. Finite automata, Turing machines, models of computation, complexity, solvability, and other topics that form a foundation of modern programming are discussed -first with a gentle theoretical orientation, and then applied through programming code and practical examples. JFLAP projects and applications are integrated throughout the book, and C# is used for all code.

The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.

Automata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.

This thesis is devoted to studying synchronizing words for finite automata and variable-length codes. Intuitively, a synchronizing word is a word such that its application brings a system into some particular state regardless of its initial state. A code or automaton is synchronizing if it admits a synchronizing word. There is a deep connection between the concrete implementations of this notion for finite automata and variable-length codes, and the use of it is one of the leitmotifs of this thesis.One of the main tools for dealing with variable-length codes is assigning a special automaton preserving many synchronization properties to it. For finite codes, this is done using prefix automata.We investigate two fundamental problems about synchronization. The first one is measuring the length of shortest synchronizing words for synchronizing automata and codes. For the case of complete deterministic finite automata, the Černý conjecture, one of the oldest problems in combinatorial automata theory, proposes a quadratic upper bound in terms of the number of states in the automaton. We broaden this conjecture to partial deterministic finite automata and then to unambiguous non-deterministic finite automata. We show polynomial upper bounds for mentioned classes in the presence of strong connectivity, and discuss their connections with the original Černý conjecture.The relation with finite codes allows us to show similar bounds in terms of the sum of the lengths of the codewords, as well as in terms of the length of the longest codeword. The second case is related to another important conjecture stated by Restivo. It deals with mortal words instead of synchronizing ones, the case which we also investigate. For most of these settings we also examine the computational complexity of finding short synchronizing words, which is the second fundamental question investigated in this thesis. Besides that, we study various generalization of the notion of a synchronizing word, which allow to use some partial information about the current state of an automaton. For several such generalizations we show strong computational complexity lower bounds even in very restricted cases.

For upper level courses on Automata. Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-ranging coverage allows instructors to easily customise course material to fit their unique requirements.