## Circuits with Medium Fan-In

Speaker: Anup Rao , University of Washington

Date: Tuesday, April 15, 2014

Time: 4:15 PM to 5:15 PM Note: all times are in the Eastern Time Zone

Refreshments: 3:45 PM

Public: Yes

Location: 32-G449

Event Type:

Room Description:

Host: Ankur Moitra, CIS, TOC, CSAIL, MIT

Contact: Holly A Jones, hjones01@csail.mit.edu

Relevant URL: http://toc.csail.mit.edu/node/486

Speaker URL: None

Speaker Photo:
None

Reminders to: seminars@csail.mit.edu, theory-seminars@csail.mit.edu, toc@csail.mit.edu

Reminder Subject: TALK: Circuits with Medium Fan-In

Abstract:

We consider boolean circuits in which every gate may compute an arbitrary boolean function of k other gates, for a parameter k. We give an explicit function f:{0,1}^n to {0,1} that requires at least Omega(log^2 n) non-input gates when k = 2n/3. When the circuit is restricted to being layered and depth 2, we prove a lower bound of n^{Omega(1)} on the number of non-input gates. When the circuit is a formula with gates of fan-in k, we give a lower bound Omega(n^2/k \log n) on the total number of gates.

Our model is connected to some well known approaches to proving lower bounds in complexity theory. Optimal lower bounds for the Number-On-Forehead model in communication complexity, or for bounded depth circuits in AC_0, or extractors for varieties over small fields would imply strong lower bounds in our model. On the other hand, new lower bounds for our model would prove new time-space tradeoffs for branching programs and impossibility results for (fan-in 2) circuits with linear size and logarithmic depth. In particular, our lower bound gives a different proof for a known time-space tradeoff for oblivious branching programs.

Joint work with Pavel Hrubes.

Research Areas:

Impact Areas:

See other events that are part of the Theory of Computation Colloquium - 2014.

Created by Holly A Jones at Friday, April 04, 2014 at 2:09 PM.