EbDa: A new theory on design and verification of deadlock-free interconnection networks

Freedom from deadlock is one of the most important issues when designing routing algorithms in on-chip/off-chip networks. Many works have been developed upon Dally's theory proving that a network is deadlock-free if there is no cyclic dependency on the channel dependency graph. However, finding such acyclic graph has been very challenging, which limits Dally's theory to networks with a low number of channels. In this paper, we introduce three theorems that directly lead to routing algorithms with an acyclic channel dependency graph. We also propose the partitioning methodology, enabling a design to reach the maximum adaptiveness for the n-dimensional mesh and k-ary n-cube topologies with any given number of channels. In addition, deadlock-free routing algorithms can be derived ranging from maximally fully adaptive routing down to deterministic routing. The proposed theorems can drastically remove the difficulties of designing deadlock-free routing algorithms.