Distributed Computability

As today Computer Science is more and more (driven) consumed by its applications, it becomes more and more important to know what is and what is not computable. For a long time now, this has been relatively well understood in sequential computing. But today the computing world becomes more and more distributed, and consequently more and more applications are distributed. As a result, it becomes important, or even crucial, to understand what is distributed computing and which are its power and its limits. This article is a step in this direction from an agreement-oriented and fault-tolerance perspective.

Distributed Computing Column 82 Distributed Computability

Overview. In this edition of the column, we have a very useful and interesting piece from Michel Raynal (IRISA Rennes & Hong Kong Polytechnic), whose goal is to provide a systematic view of the computability results in distributed computing which should be well-understood by any Masters-level student with an interest in our area. Michel's motivation for the column is that, given the intense proliferation of computational models, tasks, and correctness and progress conditions in recent years, for instance, in the context of Blockchain technology, it may be hard for newcomers to the field to understand the boundary between what is essentially possible and what is impossible in a distributed system.

Back to the Coordinated Attack Problem

We consider the well-known Coordinated Attack Problem, where two generals have to decide on a common attack, when their messengers can be captured by the enemy. Informally, this problem represents the difficulties to agree in the presence of communication faults. We consider here only omission faults (loss of message), but contrary to previous studies, we do not to restrict the way messages can be lost, i.e., we make no specific assumption, we use no specific failure metric. In the large subclass of message adversaries where the double simultaneous omission can never happen, we characterize which ones are obstructions for the Coordinated Attack Problem. We give two proofs of this result. One is combinatorial and uses the classical bivalency technique for the necessary condition. The second is topological and uses simplicial complexes to prove the necessary condition. We also present two different Consensus algorithms that are combinatorial (resp. topological) in essence. Finally, we analyze the two proofs and illustrate the relationship between the combinatorial approach and the topological approach in the very general case of message adversaries. We show that the topological characterization gives a clearer explanation of why some message adversaries are obstructions or not. This result is a convincing illustration of the power of topological tools for distributed computability.