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Basic Complexity Eric Allender

Summary: Basic Complexity
Eric Allender
Catherine McCartin
Abstract. This paper summarizes a series of three lectures the first author was in-
vited to present at the NZMRI summer 2000 workshop, held in Kaikoura, New Zealand.
Lecture 1 presents the goals of computational complexity theory. We discuss (a) what
complexity provably can never deliver, (b) what it hopes to deliver but thus far has not,
and finally (c) where it has been extremely successful in providing useful theorems. In so
doing, we introduce nondeterministic Turing machines. Lecture 2 presents alternation, a
surprisingly-useful generalization of nondeterminism. Using alternation, we define more
complexity classes, and inject clarity into a confusing situation. In Lecture 3 we present
a few of the most beautiful results in computational complexity theory. In particular, we
discuss (a) the algebraic approach to circuit complexity, (b) circuit lower bounds, and
(c) derandomization.
1. Lecture 1
Warning: This brief survey cannot take the place of a comprehen-
sive textbook. Readers looking for a more detailed account of the
topics introduced here may wish to consult books such as [HU79,
BDG95, BDG90, Vol99, Pap94, DK00] or survey chapters such as
[ALR99, BS90].


Source: Allender, Eric - Department of Computer Science, Rutgers University


Collections: Computer Technologies and Information Sciences