Computation Engineering: Applied Automata Theory and Logic / Edition 1

by Ganesh Gopalakrishnan

Overview

It takes more effort to verify that digital system designs are correct than it does to design them, and as systems get more complex the proportion of cost spent on verification is increasing (one estimate is that verification complexity rises as the square of design complexity). Although this verification crisis was predicted decades ago, it is only recently that powerful methods based on mathematical logic and automata theory have come to the designers’ rescue. The first such method was equivalence checking, which automates Boolean algebra calculations.Nextcamemodelchecking,whichcanautomatically verify that designs have – or don’t have – behaviours of interest specified in temporal logic. Both these methods are available today in tools sold by all the major design automation vendors. It is an amazing fact that ideas like Boolean algebra and modal logic, originating from mathematicians and philosophers before modern computers were invented, have come to underlie computer aided tools for creating hardware designs. The recent success of ’formal’ approaches to hardware verification has lead to the creation of a new methodology: assertion based design, in which formal properties are incorporated into designs and are then validated by a combination of dynamic simulation and static model checking. Two industrial strength property languages based on tem- ral logic are undergoing IEEE standardisation. It is not only hardwaredesignand verification that is changing: new mathematical approaches to software verification are starting to be - ployed. Microsoft provides windows driver developers with verification tools based on symbolic methods.

Product Details

ISBN-13:	9781441937414
Publisher:	Springer US
Publication date:	10/29/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	472
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Mathematical Preliminaries.- Cardinalities and Diagonalization.- Binary Relations.- Mathematical Logic, Induction, Proofs.- Dealing with Recursion.- Strings and Languages.- Machines, Languages, DFA.- NFA and Regular Expressions.- Operations on Regular Machinery.- The Automaton/Logic Connection, Symbolic Techniques.- The ‘Pumping’ Lemma.- Context-free Languages.- Push-down Automata and Context-free Grammars.- Turing Machines.- Basic Undecidability Proofs.- Advanced Undecidability Proofs.- Basic Notions in Logic including SAT.- Complexity Theory and NP-Completeness.- DFA for Presburger Arithmetic.- Model Checking: Basics.- Model Checking: Temporal Logics.- Model Checking: Algorithms.- Conclusions.

Editorial Reviews

From the reviews:

"One of the constant challenges faced by computer science faculty is how to tie in the theory of computing with applications. This text attempts to do just that … . Overall, this book is a good undergraduate theory text. … It includes exercises, with software tools to aid in visualization of key ideas. … The exercises are appropriate for an undergraduate-level class. … It is a good text … ." (M. D. Derk, Computing Reviews, December, 2006)

"The book under review shows, logic and automata theory can be combined to provide powerful tools for checking computer code … . There is no doubt that the book was written with great care and that it caters for a real need. … the book is written in a very lively style, which makes reading it quite pleasurable. … many nice applications of automata that are peppered throughout the book." (S. C. Coutinho, SIGACT News, Vol. 39 (3), 2008)

From the Publisher