Michael Sipser

This book is a real gem. A coherent focus is maintained throughout, subjects are introduced in a rational order, and not a word or paragraph is wasted. The assignments at the end of the chapter are excellently selected to enhance understanding or to encourage investigation of topics which the book does not cover.

This was one of the better textbooks I had to use, in terms of aesthetics, design, layout, and materials, but I was always frustrated by its use of animistic metaphor for rigorous algorithmic processes -- a Turing machine no more "wants" or "expects" something than a rock does. At the same time, the examples were usually more illuminating than in other texts, so I can't complain too much.

Sipser starts from a treatment of basic set theory and proofs. He moves from there through regular languages & finite automata, context-free languages & pushdown automata, and on to Turing machines & the associated complexity theory (that P and NP jazz), and more. He thus builds a rigorous and pretty complete theory of computation course from the ground up, accessible to any determined reader with a little aptitude for finite math.

The end of each chapter features dozens of general show more "exercises" and more rigorous "problems". Answers are provided for a few. When an exercise or problem makes reference to the chapter text, it's always easy to locate, as "figures", "theorems", "definitions", and so on are counted in the same series -- e.g. Figure 1.4 is found just before Definition 1.5. It's a small but refreshing design choice, one of many nice design choices in this beautiful volume.

The new edition is quite expensive indeed, especially considering how small the book is. The new content since the second edition consists of some corrections and minor changes, and a new section on deterministic context-free languages. If you are buying this book for a course that won't cover deterministic CFL's -- a very challenging topic -- you might ask your instructor for permission to use the second edition. The new material does have some relevance to compilers, though, so you might like to have it handy if you plan to study compilers later. show less

This is quite possibly one of the most terse, clearly-written CS theory books that there is.