Fractional Pebbling Game Lower Bounds

TL;DR

This paper establishes a tight lower bound on the pebble weight needed for fractional pebbling of balanced d-ary trees, linking it to computational complexity and space lower bounds.

Contribution

It solves an open problem by providing a precise lower bound for fractional pebbling on balanced d-ary trees, advancing understanding in computational complexity.

Findings

Proves a tight lower bound on fractional pebbling weight.

Links fractional pebbling bounds to branching program complexity.

Contributes to separating complexity classes P and NL.

Abstract

Fractional pebbling is a generalization of black-white pebbling introduced recently. In this reasearch paper we solve an open problem by proving a tight lower bound on the pebble weight required to fractionally pebble a balanced d-ary tree of height h. This bound has close ties with branching programs and the separation of P from NL.