13,600 research outputs found
Foundation to Promote Scholarship and Teaching 2009-2010 Awards
Proposal abstracts of 2009-2010 award recipients in a wide range of disciplinary areas
Foundation to Promote Scholarship and Teaching 2012-2013 Awards
Proposal abstracts of 2012-2013 award recipients in a wide range of disciplinary areas
Foundation to Promote Scholarship and Teaching 2013-2014 Awards
Proposal abstracts of 2013-2014 award recipients in a wide range of disciplinary areas
Quantified Derandomization of Linear Threshold Circuits
One of the prominent current challenges in complexity theory is the attempt
to prove lower bounds for , the class of constant-depth, polynomial-size
circuits with majority gates. Relying on the results of Williams (2013), an
appealing approach to prove such lower bounds is to construct a non-trivial
derandomization algorithm for . In this work we take a first step towards
the latter goal, by proving the first positive results regarding the
derandomization of circuits of depth .
Our first main result is a quantified derandomization algorithm for
circuits with a super-linear number of wires. Specifically, we construct an
algorithm that gets as input a circuit over input bits with
depth and wires, runs in almost-polynomial-time, and
distinguishes between the case that rejects at most inputs
and the case that accepts at most inputs. In fact, our
algorithm works even when the circuit is a linear threshold circuit, rather
than just a circuit (i.e., is a circuit with linear threshold gates,
which are stronger than majority gates).
Our second main result is that even a modest improvement of our quantified
derandomization algorithm would yield a non-trivial algorithm for standard
derandomization of all of , and would consequently imply that
. Specifically, if there exists a quantified
derandomization algorithm that gets as input a circuit with depth
and wires (rather than wires), runs in time at
most , and distinguishes between the case that rejects at
most inputs and the case that accepts at most
inputs, then there exists an algorithm with running time
for standard derandomization of .Comment: Changes in this revision: An additional result (a PRG for quantified
derandomization of depth-2 LTF circuits); rewrite of some of the exposition;
minor correction
A socio-linguistic theory of closing the gap in Scottish schools
Peer reviewedPublisher PD
Methodology for Process Improvement Through Basic Components and Focusing on the Resistance to Change.
This paper describes a multi-model methodology that implements a smooth and continuous process improvement, depending on the organization's business goals and allowing users to establish their improvement implementation pace. The methodology focuses on basic process components known as ‘best practices’. Besides, it covers following the topics: knowledge management and change management. The methodology description and the results of a case study on project management process are included
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