Brief Announcement: Synchronous Las Vegas URMT Iff Asynchronous Monte Carlo URMT

Introduction

In the unconditionally reliable message transmission (URMT) problem, two non-faulty nodes, the sender S and the receiver R are part of a communication network modelled as a digraph over a set of nodes influenced by an unbounded active adversary that may corrupt some subset of these nodes. S has a message that he wishes to send to R; the challenge is to design a protocol such that R correctly obtains S’s message with arbitrarily high probability, irrespective of what the adversary (maliciously) does to disrupt the protocol. Analogous to randomized sequential algorithms, one may distinguish between two variants of URMT, namely, Monte Carlo and Las Vegas. In the former variant R outputs the sender’s message with high probability and may produce an incorrect output with small probability; in the latter, R outputs the sender’s message with high probability and with small probability may abort the protocol but in no case does the receiver terminates with an incorrect output.

In this work, we focus on studying the (im)possibility of Monte Carlo URMT protocols over asynchronous networks (U _AMC ) and Las Vegas URMT protocols over synchronous networks (U _SLV ). Though not seemingly related, interestingly, we show that the network connectivity requirements for both the aforementioned cases are same (and are strictly greater than that of Monte Carlo protocols over synchronous networks, which has been studied in [4]).