2 research outputs found
Simultaneous Multiparty Communication Protocols for Composed Functions
In the Number On the Forehead (NOF) multiparty communication model,
players want to evaluate a function on some input by broadcasting bits according to a
predetermined protocol. The input is distributed in such a way that each player
sees all of it except . In the simultaneous setting, the players
cannot speak to each other but instead send information to a referee. The
referee does not know the players' input, and cannot give any information back.
At the end, the referee must be able to recover from what
she obtained.
A central open question, called the barrier, is to find a function
which is hard to compute for or more players (where the 's
have size ) in the simultaneous NOF model. This has important
applications in circuit complexity, as it could help to separate from
other complexity classes. One of the candidates belongs to the family of
composed functions. The input to these functions is represented by a boolean matrix , whose row is the input and is a
block-width parameter. A symmetric composed function acting on is specified
by two symmetric - and -variate functions and , that output
where is the -th block of width
of . As the majority function is conjectured to be outside of
, Babai et. al. suggested to study , with large
enough.
So far, it was only known that is not enough for to
break the barrier in the simultaneous deterministic NOF model. In this
paper, we extend this result to any constant block-width , by giving a
protocol of cost for any symmetric composed
function when there are players.Comment: 17 pages, 1 figure; v2: improved introduction, better cost analysis
for the 2nd protoco