Pebbling and Branching Programs Solving the Tree Evaluation Problem

We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted, balanced binary tree of height h, whose internal nodes are labeled with binary functions on [k] = {1,...,k} (each given simply as a list of k^2 elements of [k]), and whose leaves are labeled with elements of [k]. Each node obtains a value in [k] equal to its binary function applied to the values of its children, and the output is the value of the root. The first restricted computation model, called Fractional Pebbling, is a generalization of the black/white pebbling game on graphs, and arises in a natural way from the search for good upper bounds on the size of nondeterministic branching programs (BPs) solving the TEP - for any fixed h, if the binary tree of height h has fractional pebbling cost at most p, then there are nondeterministic BPs of size O(k^p) solving the height h TEP. We prove a lower bound on the fractional pebbling cost of d-ary trees that is tight to within an additive constant for each fixed d. The second restricted computation model we study is a semantic restriction on (non)deterministic BPs solving the TEP - Thrifty BPs. Deterministic (resp. nondeterministic) thrifty BPs suffice to implement the best known algorithms for the TEP, based on black (resp. fractional) pebbling. In earlier work, for each fixed h a lower bound on the size of deterministic thrifty BPs was proved that is tight for sufficiently large k. We give an alternative proof that achieves the same bound for all k. We show the same bound still holds in a less-restricted model, and also that gradually weaker lower bounds can be obtained for gradually weaker restrictions on the model.Comment: Written as one of the requirements for my MSc. 29 pages, 6 figure

2011 Outlook Report

To assess the outlook for grantmaking in Minnesota in 2011, the Minnesota Council on Foundations (MCF) conducted its 2011 Outlook Report survey in October and November of 2010. The survey asked grantmakers to predict how their 2011 giving will compare to 2010. A total of 118 organizations responded, representing about 65 percent of annual grantmaking in the state. Foundation giving is expected to stabilize in 2011 following two years in which grantmakers anticipated declines. According to MCF's 2011 Outlook Report survey, indicators also signal that Minnesota grantmakers are more optimistic about their giving in 2011 than they were at this time last year

2009 Outlook Report

What is the outlook for grantmaking in Minnesota for 2009? In November 2008, the Minnesota Council on Foundations (MCF) surveyed its members, as well as nonmember foundations and giving programs that are among the top 100 grantmakers in the state, to determine how economic changes may affect grantmaking activity in the coming year. Our survey results point toward some dramatic shifts in anticipated grantmaking for 2009. Assets are declining and are expected to decline further in 2009. Accordingly, grantmakers are expecting giving to decline. While grantmaking is decreasing at a somewhat lower rate than that of assets because payouts are typically based on one- to three-year rolling averages, this same factor may negatively affect grant levels in 2010 and beyond. To ease the impact on nonprofits, all types of foundations and corporate giving programs are exploring other opportunities for support, including increasing in-kind giving and offering other non-monetary assistance

Giving in Minnesota, 2008 Edition

The Minnesota Council on Foundations has produced Giving in Minnesota, 2008 Edition to provide a comprehensive analysis of philanthropy in the state. The 2008 edition features overall giving in 2006, the most recent year for which comprehensive data are available. This summary provides highlights from the full report, which includes information about overall giving by foundations, corporations and individuals in Minnesota, along with detailed grantmaking trends by the Giving in Minnesota sample, which is comprised of 100 of the state's largest grantmakers based on grants paid. Although the foundations and corporate giving programs in the sample represented just 7 percent of grantmakers in the state, they gave 81 percent of all Minnesota grant dollars in 2006. Trend analysis focused on the sample's $815 million given as grants of$2,000 or more

Correcting Errors in the Bostrom/Kulczycki Simulation Arguments

Both patched versions of the Bostrom/Kulczycki simulation argument contain serious objective errors, discovered while attempting to formalize them in predicate logic. The English glosses of both versions involve badly misleading meanings of vague magnitude terms, which their impressiveness benefits from. We fix the errors, prove optimal versions of the arguments, and argue that both are much less impressive than they originally appeared. Finally, we provide a guide for readers to evaluate the simulation argument for themselves, using well-justified settings of the argument parameters that have simple, accurate statements in English, which are easier to understand and critique than the statements in the original paper