On Teaching the Basics of Complexity Theory

We outline a conceptual framework for teaching the basic notions and results of complexity theory. Our focus is on using definitions and on organizing the presentation in a way that reflects the fundamental nature of the material. We do not attempt to provide a self-contained presentation of the material itself, but rather outline our (non-innovative) suggestions regarding how this material should be presented in class. We discuss the P-vs-NP Question, the general notion of a reduction, and the theory of NP-completeness. In particular, we suggest to present the P-vs-NP Question both in terms of search problems and in terms of decision problems (where NP is viewed as a class of proof systems). As for the theory of NP-completeness, we suggest to highlight the mere existence of NP-complete sets