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 k2 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. 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 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 branching programs o...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Dustin Wehr
• Keywords: Branching Programs, Computation Model, CORR 2010, Education, Nondeterministic Branching Programs