Functions in arithmetic NC1 are known to have equivalent constant width polynomial degree circuits, but the converse containment is unknown. In a partial answer to this question, we show that syntactic multilinear circuits of constant width and polynomial degree can be depth-reduced, though the resulting circuits need not be syntactic ... more >>>

The parallel complexity class NC^1 has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. \cite{CMTV} considered arithmetizations of two of these classes, #NC^1 and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths ... more >>>