We study shared randomness in the context of multi-party number-in-hand communication protocols in the simultaneous message passing model. We show that with three or more players, shared randomness exhibits new interesting properties that have no direct analogues in the two-party case.

First, we demonstrate a hierarchy of modes of shared ... more >>>

We propose that multi-linear functions of relatively low degree
over GF(2) may be good candidates for obtaining exponential
lower bounds on the size of constant-depth Boolean circuits
(computing explicit functions).
Specifically, we propose to move gradually from linear functions
to multilinear ones, and conjecture that, for any $t\geq2$,
more >>>

The two-player pebble game of Dymond–Tompa is identified as a barrier for existing techniques to save space or to speed up parallel algorithms for evaluation problems.

Many combinatorial lower bounds to study L versus NL and NC versus P under different restricted settings scale in the same way as the ... more >>>