Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

Investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories, such as those of semigroups, groups, rings, and fields. The authors also investigate automata networks as products of automata, that is, as compositions of automata obtained by cascading without feedback or with feedback of various restricted types or, most generally, with the feedback dependencies controlled by an arbitrary directed graph. They survey and extend the fundamental results in regard to automata networks, including the main decomposition theorems of Letichevsky, of Krohn and Rhodes, and of others.

The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases.

Semigroups, Automata, Universal Algebra, Varieties

Learn to identify the implementation of Discrete Structure and Theory of Automata in a myriad of applications used in day to day lifeKey Featuresa- Learn how to write an argument using logical notation and decide if the argument is valid or not valid.a- Learn how to use the concept of different data structures (stacks, queues, sorting concept, etc.) in the computer science field.a- Learn how to use Automata Machines like FSM, Pushdown automata, Turing machine, etc. in various applications related to computer science through suitable practical illustration.a- Learn how to implement the finite state machine using JFLAP (Java Formal Languages and Automata Package).DescriptionThis book's purpose is to provide a modern and comprehensive introduction to the subject of Discrete Structures and Automata Theory. Discrete structures, also called Discrete Mathematics, are an exciting and active subject, particularly due to its extreme relevance to both Mathematics and Computer Science and Algorithms. This subject forms a common foundation for rigorous Mathematical, Logical Reasoning and Proofs, as well as a formal introduction to abstract objects that are essential tools in an assortment of applications and effective computer implementations. Computing skills are now an integral part of almost all the Scientific fields, and students are very enthusiastic about being able to harness the full computing power of these tools. Further, this book also deep dives into the Automata Theory with various examples that illustrate the basic concepts and is substantiated with multiple diagrams. The book's vital feature is that it contains the practical implementation of the Automata Machine example through the JFLAP Tool. Courses on Discrete Structures and Automata theory are offered at most universities and colleges.What will you learna- Understand the basic concepts of Sets and operations in Sets.a- Demonstrate different traversal techniques for Trees and Graphs.a- Deep dive into the concept of Mathematical Induction, Sets, Relations, Functions, Recursion, Graphs, Trees, Boolean Algebra, and Proof techniques.a- Understand the concept of Automata Machines in day to day life like the Elevator, Turnstile, Genetic Algorithms, Traffic lights, etc.a- Use the JFLAP tool to solve the various exercise problems related to automata theory.Who this book is forThis book is a must-read to everyone interested in improving their concepts regarding Discrete Structure and Automata Theory.Table of Contents1. Set Theory2. Relations and Functions3. Graph Theory4. Trees5. Algebraic Structure6. Recursion and Recurrence Relations7. Sorting8. Queues9. Introduction10. Finite Automata Theory11. Theory of Machines12. Regular Language13. Grammar14. Pushdown Automata15. Cellular Automata16. Turning Machine17. Problems Solving Using JFLAP Tool18. Revision QuestionsAbout the AuthorsDr. UMESH SEHGAL completed his Ph.D.,M.Phil. Computer Science and MCA. He held academic positions at the GNA University as an A.P in FCS Department. He has achieved the Best Educationist Award in 2017.He has achieved the Indira Gandhi Education Excellence Award in 2017.He has achieved the Best Researcher Award in 2018-19.He has published several articles in leading International and National Computer science journals and has been an invited speaker at Wireless networks based lectures and conferences in the many universities and Institutes in India, Malaysia, China, and UAE.SUKHPREET KAUR GILL received the M.Tech. degree in Computer Science and Engineering from Guru Nanak Dev Engineering College, Ludhiana. She is currently working as Assistant Professor at GNA University Phagwara. She has achieved the Bright Educator Award 2019. She has published several articles in leading International and National Computer science journals.

The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases.

Discrete Structures and Automata Theory is designed for an introductory course on formal languages, automata and discrete mathematics. Divided into two parts it covers discrete methods - stressing the finite nature in many problems and structures; combinatorics - the algebra of enumeration or coding and finite algebraic structures - effecting coding theory, method of enumeration, gating networks and combinatorial designs. It also discusses the applications of Automata Theory in Compiler design, Natural Language Processing and development of new programming languages.