Sciweavers

Share
FSTTCS
2009
Springer

Fractional Pebbling and Thrifty Branching Programs

11 years 8 months ago
Fractional Pebbling and Thrifty Branching Programs
We study the branching program complexity of the tree evaluation problem, introduced in [BCM+09a] as a candidate for separating NL from LogCFL. The input to the problem is a rooted, balanced dary tree of height h, whose internal nodes are labelled with d-ary functions on [k] = {1, . . . , k}, and whose leaves are labelled with elements of [k]. Each node obtains a value in [k] equal to its d-ary function applied to the values of its d children. The output is the value of the root. Deterministic k-way branching programs as related to black pebbling algorithms have been studied in [BCM+09a]. Here we introduce the notion of fractional pebbling of graphs to study nondeterministic branching program size. We prove that this yields non-deterministic branching programs with Θ(kh/2+1) states solving the Boolean problem “determine whether the root has value 1” for binary trees - this is asymptotically better than the branching program size corresponding to black-white pebbling. We prove upp...
Mark Braverman, Stephen A. Cook, Pierre McKenzie,
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where FSTTCS
Authors Mark Braverman, Stephen A. Cook, Pierre McKenzie, Rahul Santhanam, Dustin Wehr
Comments (0)
books