Models of Computation: An Introduction to Computability Theory (Undergraduate Topics in Computer Science) 2009th Edition by Maribel Fernandez (PDF)

Description

A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided.Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: – Automata and Turing Machines; – Recursive functions and the Lambda-Calculus; – Logic-based computation models.and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics.At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐About me: I’m a grad student in math, but have no prior experienceof the topic of the book. I have actually not yet read the 40last pages or so, so the review is about the rest of the book.I will be quite negative below, so I want to start by sayingthat most chapters are OK, and I love short books. And thisbook gives you a quick way of getting aquainted with various modelsof computation. I dont agree with the official reviewer thatit goes in to depth or is extremely clear and well written.On the contrary, it does NOT go into depth in all chapters, butis rather uneven. I really liked the chapter about lambda-calculus.My general impression is that the author is often saying”how to think” about the definitions and concepts, and what theyintuitively are, rather than precisely saying what the definition IS.I believe that the cause of my confusion, other than perhaps ignorance,is the lack of crucial pieces of information. (See examples below).Many times I found myself confused after reading a definition, andreally needed an example to clarify what was going on. Althoughthere are fairly many examples in the book, there were several placesin desperate need thereof.It is mostly chapters 5 and 7 that I find confusing.Example (chapter 5, on logic programs) Definitive clauses – Program clauses and Goals – are defined. A definitive clause is P1 or (not P2 or not P3 …. or not Pn), i.e. a disjunction of so called “literals”, and atmost one literal is positive. A definitive clause is a Goal if we remove P1, i.e. we have only negative literals. The problem is that there is only a definition of what a Goal is but not what meeting a Goal is… Only a very vague and incomplete explaination is given: “Program clauses can be seen as defining a database: […] Goals are questions to be answered using the information about the problem in the database. This can be better seen with some examples.” Then there is only ONE example in which the goal has only ONE negative literal. That leaves the reader wondering if each literal P2, …., Pn should be true or just “atleast one of them”. Since the notation for a goal is :- P2,P3,…,Pn you might believe that the goal is to deduce ALL of the Pi’s, but since its a disjunction of negative literals, mathematically it only makes sense if the goal clause should be disproven, which means that ONE of the Pi’s hold. It gets even more confusing later on. Although I might have my self to blame for some of the confusion, I am pretty convinced this is far from optimally written.Other complaints:There are some flaws in the technique of writing. For example the author mentionsmultisets several times, but gives the definition only the last time. On anotherinstance a new symbol is used and defined afterwards.There is also a logical flaw on page 61. There is an argument that “bounded minimisation”of a primitive recursive predicate is also primitive recursive.The argument uses a lemma whose input are functions f_1, …, f_k that are primitive recursivetotal functions. Then the lemma is applied in a case where f_1 is a priori only partially defined.I’m sure its possible to fix this argument, but it still makes life unneccesarily difficult forthe reader.

⭐I used this textbook alongside an undergraduate computer science module and found it to be be very helpful with my studies. The author is effective at communicating highly theoretical concepts in an understandable and unpretentious way. This makes the book a great introduction for those new to the subject.The book is organised clearly, each chapter relating to a different model of computation. Chapters start by briefly putting the model into context before going on to explaining the model in formal terms. Many easy to follow examples accompany the more abstract explanations.At the end of each chapter there are a number of exercises, most of which also have fully explained solutions. I found these exercises especially useful because it allowed me to test whether I had correctly understood the theoretical concepts covered in the chapter. The exercises are a good level of difficulty, encouraging independent thought.Some background in logic would help when reading the book.

⭐I found this book extremely useful when I was studying computability. It is very well written and makes a “difficult” subject seem straightforward. It has well thought out examples and exercises at the end of each chapter. I’d recommend this book to anyone studying the subject whether formally or out of interest.

⭐Worst book I have ever read! AWFUL.

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