 
Summary: Arithmetic Circuits and Counting Complexity
Classes
Eric Allender
Dept. of Computer Science
Rutgers University
New Brunswick, NJ, USA
allender@cs.rutgers.edu
November 26, 2004
1 Introduction
Arithmetic circuits are the focus of renewed attention in the complexity
theory community. It is easy to list a few of the reasons for the increased
interest:
· Innovative work by Kabanets and Impagliazzo [KI03] shows that, in
some cases, providing lower bounds on arithmetic circuit size can yield
consequences about Boolean complexity classes. For instance, one of
the most important problems in BPP that is not known to be in P is
Arithmetic Circuit Identity Testing (ACIT), the problem of determin
ing if two arithmetic circuits compute the same function. They show
that the Boolean complexity of this problem is intimately linked to the
arithmetic complexity of the Permanent.
