Arithmetizing Uniform NC

Arithmetizing Classes Around NC 1 and L

The parallel complexity class NC has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. [CMTV98] considered arithmetizations of two of these classes, #NC and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs over visibly pushdown automata is in FLo...

Arithmetizing classes around NC and L

The parallel complexity class NC has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. [CMTV98] considered arithmetizations of two of these classes, #NC and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs over visibly pushdown automata is in FLo...

Low uniform versions of NC

In the setting known as DLOGTIME-uniformity, the fundamental complexity classes AC ⊂ ACC ⊆ TC ⊆ NC have several robust characterizations. In this paper we refine uniformity further and examine the impact of these refinements on NC and its subclasses. When applied to the logarithmic circuit depth characterization of NC, some refinements leave NC unchanged while others collapse NC to NC. Thus we ...

Arithmetizing proofs in analysis

Arithmetizing Continuous Distributions: Numerical Aspects

This paper deals with the arithmetization of univariate and bivariate distributions, i.e. with their transformation into discrete distributions defined on the non-negative integers. Numerical aspects are investigated.