Limits of Computation ─ An Introduction to the Undecidable and the Intractable

"Preface To the student: We think that the theory dealing with what is hard about computation (and what is impossible!) is challenging but fun. This book grows out of these ideas, and our approach to teaching a course in computational complexity. There is no doubt that some of the material in these chapters is what might be called "wrap your brain around it" material, where a first reaction might be that the authors are pulling off a trick like a magician pulling a rabbit out of a hat. For instance, consider the proof--using proof by contradiction--that there can be no algorithm to tell whether a program written in C++ will go into an infinite loop. One reaction upon reaching the contradiction at the end of the proof might be that there must be a misstepsomewhere in the proof; another might be that there cannot really be a contradiction. Only after reading, rereading, and carefully considering each step can the student buy in to the proof. There are no shortcuts here; this is not reading to be done withthe television playing in the background"--

Edna E. Reiter, Ph.D., is the current Chair of the Department of Mathematics and Computer Science at California State University, East Bay (CSUEB). Her research interests include noncommutative ring theory and theoretical aspects of computer science.

Clayton Matthew Johnson, Ph.D., is the graduate coordinator for all M.S. students and the incoming Chair of the Department of Mathematics and Computer Science at CSUEB. His research interests include genetic algorithms and machine learning.

Drs. Reiter and Johnson developed the subject matter for the CSUEB Computation and Complexity course, which is required for all students in the computer science M.S. program. The course covers the hard problems of computer science—those that are intractable or undecidable. The material in this book has been tested on multiple sections of CSUEB students.