Title: Lower bounds on the randomized communication complexity of read-once functions.
Speaker: Nikos Leonardos, Rutgers University
Date: Wednesday, February 18, 2009 11:00-12:00pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
We prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae.
A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond to variables, and the internal nodes are labeled by binary connectives. Under certain assumptions, this representation is unique. Thus, one can define the depth of a formula as the depth of the tree that represents it.
The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model. In the communication complexity model, many interesting results deal with specific read-once formulae, such as DISJOINTNESS and TRIBES. In this paper we use information theory methods to prove lower bounds that hold for any read-once formula. Our lower bounds are of the form $n(f)/c^{d(f)}$, where $n(f)$ is the number of variables and $d(f)$ the depth of the formula, and they are optimal up to the constant $c$ in the denominator.
ECCC link: http://eccc.hpi-web.de/eccc-reports/2009/TR09-010/index.html