Models of Computation and Formal Languages Review

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Models of Computation and Formal Languages ReviewThe theory of computing can be a difficult subject to master, because of the densely symbolic notation and the mathematical complexity of the concepts. When I was a graduate student preparing for the theory portion of my exams, I remember being dismayed at the choice of textbooks that was available at the time: most simply threw a collection of Greek letters and subscripts at the reader, with little attempt to provide simply-worded explanations that would give the reader an intuition for the concepts.
Now that I am teaching the theory of computing, I want to provide my students with the best textbook I can find.
Two years ago, I was delighted to find R. Gregory Taylor's new book, "Models of Computation and Formal Languages". This is by far one of the most readable theory textbooks I have encountered. One of the features that caught my eye when I first examined the book was that many of the complicated symbolic expressions are accompanied by little explanatory text boxes with arrows that point to a symbol in the expression and explain the symbol that the arrow points to. I do this in class when I am lecturing -- I point to various symbols and explain where they came from, sometimes jotting down notes on the board alongside the symbols -- but this is the first time I have seen this technique in a textbook.
The writing style of the book is also fairly friendly and informal, without compromising mathematical precision.
The coverage of Turing-equivalent computing models is broader than in most introductory theory books; Taylor includes chapters not only on Turing Machines, but also on Recursive Function Theory, Markov Algorithms, Register Machines, Post Systems, and a model of parallel computation. Additionally, most chapters end with a proof that the model presented in that chapter is computationally equivalent to Turing Machines; thus, by the time the Church-Turing thesis is introduced in chapter 8, the reader is well prepared to entertain the claim that all of these models are capturing the same basic notion of an "algorithm".
I highly recommend this book to readers who want a readable introduction to computability theory.Models of Computation and Formal Languages OverviewModels of Computation and Formal Languages presents a comprehensive and rigorous treatment of the theory of computability. The text takes a novel approach focusing on computational models and is the first book of its kind to feature companion software. Deus Ex Machina, developed by Nicolae Savoiu, comprises software simulations of the various computational models considered and incorporates numerous examples in a user-friendly format. Part I of the text introduces several universal models including Turing machines, Markov algorithms, and register machines. Complexity theory is integrated gradually, starting in Chapter 1. The vector machine model of parallel computation is covered thoroughly both in text and software. Part II develops the Chomsky hierarchy of formal languages and provides both a grammar-theoretic and an automata-theoretic characterization of each language family. Applications to programming languages round out an in-depth theoretical discussion, making this an ideal text for students approaching this subject for the first time. Ancillary sections of several chapters relate classical computability theory to the philosophy of mind, cognitive science, and theoretical linguistics. Ideal for Theory of Computability and Theory of Algorithms courses at the advanced undergraduate or beginning graduate level, Models of Computation and Formal Languages is one of the only texts that... Features accompanying software available on the World Wide Web at http://home.manhattan.edu/~gregory.taylor/thcomp/ Adopts an integrated approach to complexity theory Offers a solutions manual containing full solutions to several hundred exercises. Most of these solutions are available to students on the World Wide Web at http://home.manhattan.edu/~gregory.taylor/thcomp Features examples relating the theory of computation to the probable programming experience of an undergraduate computer science major

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