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...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Mark Braverman, Stephen A. Cook, Pierre McKenzie, Rahul Santhanam, Dustin Wehr
• Keywords: Branching Program Size, Branching Programs, FSTTCS 2009, K-way Branching Programs, Theoretical Computer Science