Time, hardware, and uniformity

Abstract

We describe three orthogonal complexity measures: parallel time, amount of hardware, and degree of non-uniformity, which together parametrize most complexity classes. We show that the descriptive complexity framework neatly captures these measures using the parameters: quantifier depth, number of variable bits, and type of numeric predicates respectively. A fairly simple picture arises in which the basic questions in complexity theory-solved and unsolved-can be understood as questions about tradeoffs among these three dimensions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>