The layer complexity of Arthur-Merlin-like communication

11/09/2018
by   D. Gavinsky, et al.
0

In communication complexity the Arthur-Merlin (AM) model is the most natural one that allows both randomness and non-determinism. Presently we do not have any super-logarithmic lower bound for the AM-complexity of an explicit function. Obtaining such a bound is a fundamental challenge to our understanding of communication phenomena. In this work we explore the gap between the known techniques and the complexity class AM. In the first part we define a new natural class Small-advantage Layered Arthur-Merlin (SLAM) that have the following properties: - SLAM is (strictly) included in AM and includes all previously known sub-AM classes with non-trivial lower bounds. - SLAM is qualitatively stronger than the union of those classes. - SLAM is a subject to the discrepancy bound: in particular, the inner product function does not have an efficient SLAM-protocol. Structurally this can be summarised as SBP ∪ UAM ⊂ SLAM ⊆ AM ∩ PP. In the second part we ask why proving a lower bound of ω(√(n)) on the MA-complexity of an explicit function seems to be difficult. Both of these results are related to the notion of layer complexity, which is, informally, the number of "layers of non-determinism" used by a protocol. We believe that further investigation of this concept may lead to better understanding of the communication model AM and to non-trivial lower bounds against it.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/25/2017

Nondeterministic Communication Complexity with Help and Graph Functions

We define nondeterministic communication complexity in the model of comm...
research
03/19/2019

A New Lower Bound for Semigroup Orthogonal Range Searching

We report the first improvement in the space-time trade-off of lower bou...
research
10/09/2018

On the Relationship between Energy Complexity and Other Boolean Function Measures

In this work we investigate into energy complexity, a Boolean function m...
research
11/22/2021

On the Local Communication Complexity of Counting and Modular Arithmetic

In standard number-in-hand multi-party communication complexity, perform...
research
11/05/2017

Fooling Views: A New Lower Bound Technique for Distributed Computations under Congestion

We introduce a novel lower bound technique for distributed graph algorit...
research
03/18/2021

Lower bound the T-count via unitary stabilizer nullity

We introduce magic measures for multi-qubit quantum gates and establish ...
research
04/13/2023

Improved lower bounds for Queen's Domination via an exactly-solvable relaxation

The Queen's Domination problem, studied for over 160 years, poses the fo...

Please sign up or login with your details

Forgot password? Click here to reset