Automata and Computability - Kozen, Dexter C. (Springer, 1997)
These are my lecture notes from C8381/481: Automata and Computability Theory, a one-semester senior-level course I have taught at Cornell University for many years. I took this course myself in the fall of 1974 as a first-year Ph.D. student at Cornell from Juris Hartmanis and have been in love with the subject ever since. The course is required for computer science majors at Cornell. It exists in two forms: C8481, an honors version; and C8381, a somewhat gentlerpaced version. The syllabus is roughly the same, but C8481 goes deeper into the subject, covers more material, and is taught at a more abstract level. Students are encouraged to start off in one or the other, then switch within the first few weeks if they find the other version more suitable to their level of mathematical skill. The purpose of the course is twofold: to introduce computer science students to the rich heritage of models and abstractions that have arisen over the years; and to develop the capacity to form abstractions of their own and reason in terms of them. The course is quite mathematical in flavor, and a certain degree of previous mathematical experience is essential for survival. 8tudents should already be conversant with elementary discrete mathematics, including the notions of set, function, relation, product, partial order, equivalence relation, graph, and tree. They should have a repertoire of basic proof techniques at their disposal, including a thorough understanding of the principle of mathematical induction.
Keywords: Machine theory; Computable functions