How to Mend Garden Hose

New Bounds for the Garden-Hose Model

We show new results about the garden-hose model. Our main results include improved lower bounds based on non-deterministic communication complexity (leading to the previously unknown Θ(n) bounds for Inner Product mod 2 and Disjointness), as well as an O(n · log n) upper bound for the Distributed Majority function (previously conjectured to have quadratic complexity). We show an efficient simula...

How to Mend a Broken Heart?

What do you do to start reading how to mend a broken heart? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small w...

The Garden Hose Complexity for the Equality Function

The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in 1 ar X iv :1 31 2. 72 22 v2 [ qu an tph ] 3 0 D ec 2 01 3 the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah[MM12] with...

Position-Based Quantum Cryptography and the Garden-Hose Game

We study position-based cryptography in the quantum setting. We examine a class of protocols that only require the communication of a single qubit and 2n bits of classical information. To this end, we define a new model of communication complexity, the garden-hose model, which enables us to prove upper bounds on the number of EPR pairs needed to attack such schemes. This model furthermore opens...

How can you mend a broken heart?.