Description
Book SynopsisThis textbook is uniquely written with dual purpose. It cover cores material in the foundations of computing for graduate students in computer science and also provides an introduction to some more advanced topics for those intending further study in the area. This innovative text focuses primarily on computational complexity theory: the classification of computational problems in terms of their inherent complexity. The book contains an invaluable collection of lectures for first-year graduates on the theory of computation. Topics and features include more than 40 lectures for first year graduate students, and a dozen homework sets and exercises.
Trade ReviewFrom the reviews:
"This book represents the lecture notes of Dexter Kozen for the first-year graduate students in computer science at Cornell University. The book contains 41 primary lectures and 10 supplementary lectures covering more specialized and advanced topics. There are also 12 homework sets and several miscellaneous homework exercises … many with hints and complete solutions. … there is a bibliography of 127 titles. The book contains a very useful list of notations and abbreviations and an index." (Daniela Marinescu, Zentralblatt MATH, Vol. 1102 (4), 2007)
"The book is a collection of lecture notes based on a one-semester course for first-year graduate students in computer science at Cornell … . The course serves a dual purpose: to cover material in the foundations of computing for graduate students in computer science preparing for their Ph.D. qualifying exams, and to provide an introduction to some more advanced topics in the theory of computational complexity for those intending to pursue further study in the area." (Ulrich Tamm, Mathematical Reviews, Issue 2007 f)
"This textbook covers topics essential to the theory of computation. … In short, this is an interesting and enjoyable book that is strongly recommended to people who appreciate accuracy and concision. It will surely be an important textbook on the theory of computation for years to come. The intended audience is advanced undergraduate and first-year graduate students in computer science. It could also be useful to computer scientists with an interest in the foundation of computing and computational complexity." (G. Ciobanu, Computing Reviews, Vol. 49 (5), May, 2008)
"Kozen does a great job of explaining the material… The book is a continuation of the author’s excellent work in the field… The 12 homework sets, along with several miscellaneous problem sets, make this book an excellent pedagogical option for the classroom." (Hector Zenil, ACM Computing Reviews, Vol. 49 (9), September 2008)
Table of ContentsLectures.- The Complexity of Computations.- Time and Space Complexity Classes and Savitch’s Theorem.- Separation Results.- The Immerman-Szelepcsényi Theorem.- Logspace Computability.- The Circuit Value Problem.- The Knaster-Tarski Theorem.- Alternation.- Problems Complete for PSPACE.- The Polynomial-Time Hierarchy.- More on the Polynomial-Time Hierarchy.- Parallel Complexity.- Relation of NC to Time-Space Classes.- Probabilistic Complexity.- BPP ?2P ? ?2P.- Chinese Remaindering.- Complexity of Primality Testing.- Berlekamp’s Algorithm.- Interactive Proofs.- PSPACE IP.- IP PSPACE.- Probabilistically Checkable Proofs.- NP PCP(n3, 1).- More on PCP.- A Crash Course in Logic.- Complexity of Decidable Theories.- Complexity of the Theory of Real Addition.- Lower Bound for the Theory of Real Addition.- Lower Bound for Integer Addition.- Automata on Infinite Strings and S1S.- Determinization of ?-Automata.- Safra’s Construction.- Relativized Complexity.- Nonexistence of Sparse Complete Sets.- Unique Satisfiability.- Toda’s Theorem.- Circuit Lower Bounds and Relativized PSPACE = PH.- Lower Bounds for Constant Depth Circuits.- The Switching Lemma.- Tail Bounds.- The Gap Theorem and Other Pathology.- Partial Recursive Functions and Gödel Numberings.- Applications of the Recursion Theorem.- Abstract Complexity.- The Arithmetic Hierarchy.- Complete Problems in the Arithmetic Hierarchy.- Post’s Problem.- The Friedberg-Muchnik Theorem.- The Analytic Hierarchy.- Kleene’s Theorem.- Fair Termination and Harel’s Theorem.- Exercises.- Homework 1.- Homework 2.- Homework 3.- Homework 4.- Homework 5.- Homework 6.- Homework 7.- Homework 8.- Homework 9.- Homework 10.- Homework 11.- Homework 12.- Miscellaneous Exercises.- Hints and Solutions.- Homework 1 Solutions.- Homework 2 Solutions.- Homework 3 Solutions.- Homework 4 Solutions.- Homework 5 Solutions.- Homework 6 Solutions.- Homework 7 Solutions.- Homework 8 Solutions.- Homework 9 Solutions.- Homework 10 Solutions.- Homework 11 Solutions.- Homework 12 Solutions.- Hints for Selected Miscellaneous Exercises.- Solutions to Selected Miscellaneous Exercises.
