Mathematical Theory of Computation (Dover Books on Mathematics) by Zohar Manna (PDF)

Description

With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students.Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and algol-like programs); flowchart schemas (basic notions, decision problems, formalization in predicate calculus, and translation programs); and the fixpoint theory of programs (functions and functionals, recursive programs, and verification programs). The treamtent is self-contained, and each chapter concludes with bibliographic remarks, references, and problems.

User’s Reviews

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

⭐This 1974 text by Professor Zohar Manna at Stanford is one of my favorites, even though I’m not a computer scientist or even a modern programmer. I’ve read all of Chapters 1 on Computability, 2 on Predicate Logic, and 4 on Flowchart Schemas since last Aug 2010, all reasonably comprehensible to me and massively interesting for their own sake.Very interesting Chapter 1 covered regular expressions and finite automata in Section 1-1 and then Turing machines in several of their aspects in Sections 1-2 thru 1-5, with good additions of some of the important work of Post. Manna’s titles for the sections about the Turing machine are interesting and somewhat mysterious: 1-2 Turing Machines / 1-3 Turing Machines as Acceptors / 1-4 Turing Machines as Generators / 1-5 Turing Machines as Algorithms. Those section titles strongly piqued my interest. In section 1-4 Manna in examples developed a whole zoo of interesting primitive recursive functions, one of my several favorite things in this book.I think Chapter 2 on first-order logic, a specialty of mine, was generally well done, and at the start of Section 2-1.3 on pp. 90-91, Professor Manna wrote the clearest explanation I’ve ever seen of the logical concepts of validity, non-validity, satisfiability, and unsatisfiability. Section 2-2 on Natural Deduction showed the various sets of introduction and elimination rules for that style of deduction very well, but Manna’s many example proofs in that section were not in that natural deduction style. Section 2-3 on the important resolution procedure was thorough, but it became very abstract near the end, i.e., not closing the deal very well.Chapter 4 on Flowchart Schemas was a great look at this theoretical way of considering computation in general. Many kinds of schemata and their decision procedures were discussed thru Section 4-2. Then Section 4-3 on Formalization in Predicate Calculus rolled a lot of the methods of Section 2-1 into formalizing flowchart schemas. Difficult, but very interesting to read. Section 4-4 on Translation Problems was a highly difficult discussion of flowchart schema programs vs. recursive programs.Chapter 5 on The Fixpoint Theory of Programs looks fascinating, but that chapter is more difficult than I am willing to try reading. Omitted Chapter 3 on Verification of Programs (via flowcharts) was the most heavily applied chapter and looked rather tedious to read, so therefore I skipped it.For those interested, at end of each chapter are very many problems to work.Unfortunately, Dover took this 2003 reprinting of ‘Mathematical Theory of Computation’ out of print sometime in Spring of 2016. Partially in observance of Dover’s killing of this book, I am rereading sections 1-2 thru 1-5 of Chapter 1 on computability in Fall of 2016. In late Oct 2016, I finally started rereading Chapter 2 on computational logic. It is also six years since I read in this book before.__________________________________________________________________________While this old book is still a very interesting read and i’m still quite fond of it, it appears that more modern books covering program correctness have gone on to much more modern and even more difficult techniques. For example

⭐. Largely out of curiosity, I bought the linked book in Oct 2013 and it’s quite well done but all of similar difficulty to ‘no go’ chapter 5 of the presently reviewed book.More relevant, in 2007 Zohar Manna and Aaron Bradley co-authored a book called ‘The Calculus of Computation’ containing a lot of subjects in computational logic, several types of induction, new ways of program verification without the flow charts of the presently reviewed book, along with several other computational subjects. A rather recommended newer book partially by Zohar Manna. Mysteriously, Amazon can’t get me an embedded link for this book that I bought two copies of from them! On Mon 30Nov2015 morning, I even found ‘The Calculus of Computation’ still for sale in Amazon, so again why no embedded link?On Sat 15Dec12, a book dealer in Illinois had a copy of the original 1974 McGraw-Hill hardcover of this book, and I ordered it with an Amazon order. Looking forward to seeing that far more robust than Dover copy, but for a whopping $116! The book arrived on Mon 31Dec12 and it is a used book in quite good condition. Author Zohar Manna has been a professor at Stanford University for many years, but was at the important Weizmann Institute of Science in Rehovot, Israel when he wrote this book in early 1970s. Interesting.

⭐Not quite as new as the listing described. Had a good deal of writing on many ofbtye pages, and the binding has begun to come apart. Still, can’t complain at this price.

⭐I like it.

⭐Are you old enough to remember when Structured Programming was controversial? Dijkstra wrote “The GOTO Considered Harmful” in CACM 1968. The letter was an explanation of why the GOTO was a dangerous programming construct in mathematical terms. The math has been refined over the decades and it lead to formal correctness proof of programming, optimizing compilers, encapsulation, etc. Today, you do structured programming without even thinking about it; modern languages don’t even have a GOTO any more.But back in those days, the “cowboy coders” bitched and moaned about these terrible restrictions of “goto-less programming” and being limited to modules with one entry and one exit point, etc. Remember back then programmers wrote “GO TO “, where destination was a label variable, or “GOTO (i) label1, label2, label3” as well as the simple “GO TO ” routinely. Nobody thought about IF-THEN-ELSE, CASE/SWITCH/SELECT or RETURN constructs. They did not use WHILE or UNTIL loops when a backward GO TO would do the job.All this crap was just theory getting in the way of their practical solutions and fast code. Most programmers then did not have the math background to appreciate that Structured Programming is MUCH more than “goto-less programming” and that you can prove programs correct in the same way that you prove a theorem in any other branch of mathematics.This book is one of the most complete books on this topic and should be at least a reference book if not read cover to cover by any programmer who wants to be more than a code monkey.

⭐Yo estoy interesado en la verificación formal de programas y, este libro, proporciona la teoría que necesito. También, contiene otros temas obligados para quien se dedica a la Computación: Teoría de Autómatas, Maquinas de Turing, Expresiones Regulares…Recomendable de principio a fin. Sirve como complemento para el libro de Hopcroft.

⭐

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