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Algebraic methods for proving lower bounds in circuit Eric Allender
 

Summary: Algebraic methods for proving lower bounds in circuit
complexity
Eric Allender
Department of Computer Science
Rutgers University
New Brunswick, NJ 08903
Abstract
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 [3]. 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

  

Source: Allender, Eric - Department of Computer Science, Rutgers University

 

Collections: Computer Technologies and Information Sciences