From 4598d5740819d83849535e433905e1ed49e97e69 Mon Sep 17 00:00:00 2001 From: Jeffrey Finkelstein Date: Tue, 6 Dec 2016 15:54:50 -0500 Subject: [PATCH] Changes plural to singular when describing a family of complexity classes. --- parameterized/paranc.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/parameterized/paranc.tex b/parameterized/paranc.tex index 7e1657a..0bcd274 100644 --- a/parameterized/paranc.tex +++ b/parameterized/paranc.tex @@ -110,7 +110,7 @@ \subsection{Definition of \texorpdfstring{$\para \NC$}{paraNC}} If the depth of the circuit is instead bounded by $f(k) O(\log^d n)$, the class is denoted $\para \NC^{d \uparrow}$, a superclass of $\para \NC^d$. If the circuits are of unbounded fan-in, the classes are $\para \AC^d$ and $\para \AC^{d \uparrow}$, respectively. -The classes $\para \AC^{d \uparrow}$ were first defined in \autocite{bst15}. +The class $\para \AC^{d \uparrow}$ was first defined in \autocite{bst15}. A subtle point is that the value of the parameter $\kappa(x)$ must be non-constant but also independent of the size of the instance $x$ for the parameterized problem to be interesting. First, if $\kappa(x)$ were bounded above by a constant for each $x$, then the parameter would be irrelevant and the problem would simply be in the standard complexity class $\NC^d$.