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Applied Automata Theory provides an engineering style of presentation of some of the applied work in the field of automata theory. Topics covered range from algebraic foundations and recursive functions to regular expressions, threshold logic, and switching circuits. Coding problems and stochastic processes are also discussed, along with content addressable memories, probabilistic reliability, and Turing machines. Much emphasis is placed on engineering applications. Comprised of nine chapters, this book first deals with the algebraic foundations of automata theory, focusing on concepts such as semigroups, groups and homomorphisms, and partially ordered sets and lattices, as well as congruences and other relations. The reader is then introduced to regular expressions; stochastic automata and discrete systems theory; and switching networks as models of discrete stochastic processes. Subsequent chapters explore applications of automata theory in coding; content addressable and distributed logic memories; recursive functions and switching-circuit theory; and synthesis of a cellular computer. The book concludes with an assessment of the fundamentals of threshold logic. This monograph is intended for graduates or advanced undergraduates taking a course in information science or a course on discrete systems in modern engineering curriculum.
The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
This classic book on formal languages, automata theory, and computational complexity has been updated to present theoretical concepts in a concise and straightforward manner with the increase of hands-on, practical applications. This new edition comes with Gradiance, an online assessment tool developed for computer science. Please note, Gradiance is no longer available with this book, as we no longer support this product.
In three main divisions the book covers combinational circuits, latches, and asynchronous sequential circuits. Combinational circuits have no memorising ability, while sequential circuits have such an ability to various degrees. Latches are the simplest sequential circuits, ones with the shortest memory. The presentation is decidedly non-standard. The design of combinational circuits is discussed in an orthodox manner using normal forms and in an unorthodox manner using set-theoretical evaluation formulas relying heavily on Karnaugh maps. The latter approach allows for a new design technique called composition. Latches are covered very extensively. Their memory functions are expressed mathematically in a time-independent manner allowing the use of (normal, non-temporal) Boolean logic in their calculation. The theory of latches is then used as the basis for calculating asynchronous circuits. Asynchronous circuits are specified in a tree-representation, each internal node of the tree representing an internal latch of the circuit, the latches specified by the tree itself. The tree specification allows solutions of formidable problems such as algorithmic state assignment, finding equivalent states non-recursively, and verifying asynchronous circuits.
This book covers substantially the central ideas of a one semester course in automata theory. It is oriented towards a mathematical perspective that is understandable to non-mathematicians. Comprehension is greatly aided by many examples, especially on the Chomsky — Schützenberger theorem, which is not found in most books in this field. Special attention is given to semiautomata theory: the relationship between semigroups and sequential machines (including Green's relations), Schützenberger's maximal subgroup, von Neumann inverses, wreath products, transducers using matrix notation, shuffle and Kronecker shuffle products. Methods of formal power series, the ambiguity index and linear languages are discussed. Core material includes finite state automata, regular expressions, Kleene's theorem, Chomsky's hierarchy and transformations of grammars. Ambiguous grammars (not limited to context-free grammars) and modal logics are briefly discussed. Turing machine variants with many examples, pushdown automata and their state transition diagrams and parsers, linear-bounded automata/2-PDA and Kuroda normal form are also discussed. A brief study of Lindenmeyer systems is offered as a comparison to the theory of Chomsky.
This text strikes a good balance between rigor and an intuitive approach to computer theory. Covers all the topics needed by computer scientists with a sometimes humorous approach that reviewers found "refreshing". It is easy to read and the coverage of mathematics is fairly simple so readers do not have to worry about proving theorems.