Complexity Theory - On teaching its basics

(In Memory of Shimon Even [1935--2004])

Oded Goldreich

Material available on-line: 1st version, February 2005. [Revisions: July 2005, Aug. 2005] [in PDF].

We outline a conceptual framework for teaching the basic notions and results of complexity theory. Our focus is on using definitions (e.g., of NP) and on organizing the presentation (e.g., of NP-completeness) 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.

Related material: P, NP, and NP-completeness (draft for a textbook).
See also various exponsitions related to complexity theory and class notes for introduction to complexity theory.

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