Summary: Algebraic methods for proving lower bounds in circuit
Department of Computer Science
New Brunswick, NJ 08903
In the limited time available, it will not be possible to give a broad survey of
the variety of algebraic techniques that have been used in proving circuit lower
bounds. Instead, I will focus narrowly on a body of related results surrounding
the complexity class ACC. In particular, I will cover the following:
· Barrington's characterization of NC1
in terms of bounded-width branching
programs . This characterization highlights the importance for circuit
complexity of the algebraic notion of solvability.
· The characterizations in [3, 5] of ACC in terms of circuits with MODgates
and in terms of solvable algebras.
· The results of [9, 11] giving lower bounds on the size required for circuits
with , , and MODp gates to compute MODq for q = p.
· The results of [14, 6] giving efficient simulations of ACC circuits by circuits