Elements of computability, decidability, and complexity (Third edition)

These lecture notes are intended to introduce the reader to the basic notions of computability theory, decidability, and complexity. More information on these subjects can be found in classical books such as [Cut80,Dav58,Her69,HoU79,Rog67]. The results reported in these notes are taken from those books and in various parts we closely follow their style of presentation. The reader is encouraged to look at those books for improving his/her knowledge on these topics. Some parts of the chapter on complexity are taken from the lecture notes of a beautiful course given by Prof. Leslie Valiant at Edinburgh University, Scotland, in 1979. It was, indeed, a very stimulating and enjoyable course. For the notions of Predicate Calculus we have used in this book the reader may refer to [Men87]. I would like to thank Dr. Maurizio Proietti at IASI-CNR (Roma, Italy), my colleagues, and my students at the University of Roma Tor Vergata and, in particular, Michele Martone. They have been for me a source of continuous inspiration and enthusiasm. Finally, I would like to thank Dr. Gioacchino Onorati and Lorenzo Costantini of the Aracne Publishing Company for their helpful cooperation.