## Integer NC^1 is equal to Boolean NC^1

### Author: Stephen Bloch

ABSTRACT

We show that the product of $n$ $3 \times 3$ matrices of $n$-bit integers can be computed in $P$-uniform $FNC^1$. Since this problem is complete~\cite{BOC:const_registers} for formul\ae\ in $\{+, \cdot\}$ on $n$-bit integers, we conclude that algebraic $NC^1$'' on integers is equal to the usual Boolean notion of $NC^1$ functions.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-23.ps.gz