I am primarily interested in the NP problem (What is the power of nondeterminism?),
the BPP problem (What is the power of randomness?), and complexity in analysis
(especially geometric measure theory). I have developed three
analytic tools for investigating these problems:
These are complexity-theoretic generalizations of classical Baire category, Lebesgue measure, and Hausdorff dimension
(fractal dimension), respectively. Each provides a mathematical means of quantifying the sizes of
subsets of various complexity classes.
Resource-bounded category (1987)
Resource-bounded measure (1991)
Resource-bounded dimension (2000)
In recent years, many investigators have worked with these
tools, extending them and using them to shed new light on
a wide variety of topics in computational complexity.
I enjoy being a part of this ongoing effort.
John Hitchcock maintains online bibliographies on resource-bounded
measure and effective
fractal dimensions, with links to available papers in the latter.