Our basic text for standard complexity theory will be my manuscript, Introduction to Complexity Classes, which you can download.

For the theory of real computation, we will use ``Computational Complexity of Real Function'' by Ker-I Ko, Birkhauser-Boston, 1991. From the publisher, it costs $98. I got a good second-hand for $34. I have asked our Library to purchase a copy. Ko has a site ker-i ko which has two more recent surveys on the area.

For quantum complexity, we will provide our own lecture notes.

Other suggested references:


  1. ``Computational Complexity'' by Christos Papadimitriou, Addison-Wesley (1994). Book Errata (local copy) This book has a fairly good introduction to the logic aspects of complexity theory, but we will not need it.
  2. ``Intro to the Theory of Computation'' by Michael Sipser, PWS Publishing (1997). This book is a good place to pick up the basics in finite automata, formal languages and recursive function theory.
  3. ``Theory of Computational Complexity'' by Ding-Zhu Du and Ker-I Ko. John Wiley & Sons, Inc. (2000).
  4. ``The Complexity Theory Companion'' by Lane A. Hemaspaandra and Mitsunori Ogihara. Springer-Verlag, 2002. (ISBN 3-540-67419-5)


  1. ``Computable Analysis'' by Klaus Weihrauch. Springer, Berlin, 2000. (ISBN 3-540-66817-9) This explains the analytic approach to real computation. Weihrauch has an introductory book availablable on the web.
  2. ``Complexity and Real Computations'' by L.Blum, F.Cucker, M.Shub and S.Smale. Springer, New York, 1998. This explains the algebraic approach to real computation.


  1. ``Quantum Computation and Quantum Information'' by Michael A. Nielsen and Isaac L. Chuang. Cambridge University Press, 2000.
  2. ``Quantum Computing'' by Jozef Gruska, McGraw-Hill (1999).