Message-efficient omission-tolerant consensus with limited synchrony

We study the problem of consensus in the general omission failure model, i.e., in systems where processes can crash and omit messages while sending or receiving. This failure model is motivated from a smart card-based security framework in which certain security problems can be reduced to consensus in that model. We propose an algorithm that solves consensus based on very weak timing assumptions. More precisely, we show that consensus is solvable using an eventual bisource and a majority of fault-free processes. An eventual bisource is a fault-free process that can eventually communicate with all other processes in a timely manner. In contrast to previous work, we use timing assumptions directly in the algorithm and do not employ the notion of a failure detector. We argue that this is helpful in reducing the message complexity, a critical aspect of algorithms which run on smart cards.