Multiparty Communication Complexity: Very Hard Functions

Construction of very hard functions for multiparty communication complexity

We consider the multiparty communication model deened in 4] using the formalism from 8]. First, we correct an inaccuracy in the proof of the fundamental result of 6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nonde-termi...

Multiparty communication complexity and very hard functions

A boolean function f(x1, . . . , xn) with xi ∈ {0, 1}m for each i is hard if its nondeterministic multiparty communication complexity (introduced in [in: Proceedings of the 30th IEEE FOCS, 1989, p. 428–433]), C(f), is at least nm. Note that C(f) nm for each f(x1, . . . , xn) with xi ∈ {0, 1}m for each i. A boolean function is very hard if it is hard and its complementary function is also hard. ...

Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity

There are three different types of nondeterminism in quantum communication: i) NQP-communication, ii) QMA-communication, and iii) QCMA-communication. In this paper we show that multiparty NQP-communication can be exponentially stronger than QCMA-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue tha...

Contents The Stretch Factor of L 1 - and L ∞ - Delaunay Triangulations 3 The NOF Multiparty Communication Complexity of Composed Functions 3 Spectral Norm of Symmetric Functions

Robust Non-interactive Multiparty Computation Against Constant-Size Collusion

Non-Interactive Multiparty Computations (Beimel et al., Crypto 2014) is a very powerful notion equivalent (under some corruption model) to garbled circuits, Private Simultaneous Messages protocols, and obfuscation. We present robust solutions to the problem of Non-Interactive Multiparty Computation in the computational and information-theoretic models. Our results include the first efficient an...