## Diagonalization (2000)

### BibTeX

@MISC{Fortnow00diagonalization,

author = {Lance Fortnow},

title = {Diagonalization},

year = {2000}

}

### OpenURL

### Abstract

We give a modern historical and philosophical discussion of diagonalization as a tool to prove lower bounds in computational complexity. We will give several examples and discuss four possible approaches to use diagonalization for separating logarithmic-space from nondeterministic polynomial-time. 1 Introduction The greatest embarrassment in computational complexity theory comes from our inability to achieve signicant complexity class separations. In recent years we have seen many interesting results come from an old technique|diagonalization. Deceptively simple, diagonalization, combined with techniques for collapsing classes, can yield quite interesting lower bounds on computation. In 1874, Cantor [Can74] rst used diagonalization for showing the set of reals is not countable. The proof worked by assuming an enumeration of the reals and designing a set that one-by-one is dierent from every set in the enumeration. Drawn as a table this process considers the diagonal set and re...