Fundamentals of Computing

These are notes for the course CS-172 I first taught in the Fall 1986 at UC Berkeley and subsequently at Boston University. The goal was to introduce the undergraduates to basic concepts of Theory of Computation and to provoke their interest in further study. Model-dependent effects were systematically ignored. Concrete computational problems were considered only as illustrations of general principles. The notes (prepared by the students and revised by me) are skeletal: they do have (terse) proofs, but exercises, references, intuitive comments and examples are missing or inadequate. The better is English in a paragraph the smaller was my contribution and the greater caution is needed. The notes can be used by an instructor designing a course or by students who either know the material and want to refresh the memory or are exceptionally bright and have access to an instructor for questions. Each subsection takes about a week of the course. A version of this notes appeared in SIGACT News; 22(1) 1991, 27(3) 1996. The most recent version is at http://www.cs.bu.edu/fac/lnd/toc/ (z.ps, z.pdf, or z.dvi). Acknowledgments. I am grateful to the University of California at Berkeley, its MacKey Professorship fund and Manuel Blum who made possible for me to teach this course. The opportunity to attend lectures of M. Blum and Richard Karp and many ideas of my colleagues at BU and MIT were very beneficial for my lectures. I am also grateful to the California Institute of Technology for a semester with light teaching load in a stimulating environment enabling me to rewrite the students’ notes. NSF grants #DCR-8304498, DCR-8607492, CCR-9015276 also supported the work. And most of all I am grateful to the students who not only have originally written these notes, but also influenced the lectures a lot by providing very intelligent reactions and criticism.